just tested a config which uses the values send by MQTT directly to decide which icon to display:

var mqttHook = [
    {
      mqttTopic: "magicmirror/tarrif/set",
      mqttPayload: [
        {
          mqttNotiCmd: ["energy_tarrif_value"]
        }
      ]
    }
  ];
var mqttNotiCommands = [
    {
      commandId: "energy_tarrif_value",
      notiID: "ENERGY_TARRIF"
    }
  ];

  module.exports = { mqttHook,  mqttNotiCommands};

{
	module: "MMM-MQTTbridge",
	disabled: false,
	config: {
		mqttServer: "mqtt://my_user:my_pass@my_server:the_port",
		mqttConfig: {
			listenMqtt: true,
		},
	}
},
{
	module: "MMM-ValuesByNotification",
	position: "top_left",
	header: "Energy",
	config: {
		updateInterval: 10,
		reuseCount: 90,
		valuePositions: "i",
		valueNaPositions: "i",
		itemPositions: "e",
		groupPositions: "e",
		groups: [
			{
				items: [
					{
						notification: "ENERGY_TARRIF",
						valueImgIcon: "modules/MMM-ValuesByNotification/icons/tom.jpg",
						values: [
							{
								jsonpath: "state",
								thresholds: [
									{
										type: "eq",
										value: "PEAK",
										valueImgIcon: "modules/MMM-ValuesByNotification/icons/peak.jpg",
									},
									{
										type: "eq",
										value: "OFF-PEAK",
										valueImgIcon: "modules/MMM-ValuesByNotification/icons/off-peak.jpg",
									},
									{
										type: "eq",
										value: "NIGHT",
										valueImgIcon: "modules/MMM-ValuesByNotification/icons/night.jpg",
									},
								]
							},
						]
					},
				]
			},
		]
	},
},

Explanation…

MMM-MQTTbridge:

• The module connects to the MQTT-Server my_server to port the_port with user my_user and password my_pass
• As listenMqtt is set to true the settings in mqttDictionary.js are used which results in:
  • If a message to mqttTopic magicmirror/tarrif/set is received the message is processed by the mqttNotiCmd energy_tarrif_value
  • As no payloadValue is specified the command is called independent of the message that is send to the topic
  • As no notiPayload is set in the command configuration but the notiID ENERGY_TARRIF every time a message is received of the specified topic a notification is send to all other modules with notification id ENERGY_TARRIF and the original MQTT message as payload

MMM-ValuesByNotification:

• the module refreshes every ten seconds as updateInterval is set to 10
• if no new notification is received for a configured notification of a item but the module refreshes it will reuse the last received value for a maximum of 90 times (reuseCount)
• As valuePositions and valueNaPositions are set to i only a specified icon will be displayed instead of the value itself (which will be v or if both should be displayed vi; see Positions-Documentation for more info)
• As itemPositions and groupPositions are both set to e only the elements and no additional titles (t) or icons (i) are displayed ( see Positions-Documentation for more info)
• A single group with one item which contains one value is specified
• The values of the item use the payload of the notification with id ENERGY_TARRIF
• As default icon a image for the value (valueImgIcon) is used which has the path modules/MMM-ValuesByNotification/icons/tom.jpg (see Icon-Documentation for more details)
• The value element selects the content with jsonpath state as its value. This means the payload of the notification is parsed as JSON and the value which is used in further processing is the content of the state element. This can be everything the HomeAssistant sends but should be either PEAK, OFF_PEAK or NIGHT
• As there are thresholds specified they are validated against the previously selected state
  • If the payload is equal to (eq) to the value PEAK the path of the valueimgIcon is changed to modules/MMM-ValuesByNotification/icons/peak.jpg
  • If the payload is equal to (eq) to the value OFF_PEAK the path of the valueimgIcon is changed to modules/MMM-ValuesByNotification/icons/off-peak.jpg
  • If the payload is equal to (eq) to the value NIGHT the path of the valueimgIcon is changed to modules/MMM-ValuesByNotification/icons/night.jpg

Directly after the start the MMM-ValuesByNotification module will display the default icon. Every 10 seconds it refreshes. If a message for the specified topic is received by MMM-MQTTbridge the notification is send. The next time the module refreshes it will validate the message content and changes the icon depending on the content.

{
			module: 'MMM-MQTT',
			position: 'top_right',
			header: 'ENERGY TARRIF',
			config: {
				logging: false,
				useWildcards: false,
				mqttServers: [
					{
						address: '192.168.222.100',
						port: '1883',
						user: 'mqtt',
						password: 'password,
						subscriptions: [
							{
								topic: "magicmirror/tarrif/set",
								maxAgeSeconds: 60,
								label: "",
								conversions: [
								  {
									from: "PEAK",
									to: "<img src='modules/default/icons/peak.png' width=80px>",
								  },
								  {
									from: "OFF-PEAK",
									to: "<img src='modules/default/icons/offpeak.png' width=80px>",
								  },
								  {
									from: "NIGHT",
									to: "<img src='modules/default/icons/night.png' width=80px>",
								  },
								  {
									from: "",
									to: "#DISABLED#",
								  },
								]
							}
						]
					}
				],
			}
		},

I’ve setup mqttDictionary.js

var mqttHook = [
    {
      mqttTopic: "magicmirror/tarrif/set",
      mqttPayload: [
        {
          payloadValue: '{"state": "PEAK"}',
          mqttNotiCmd: ["Command PEAK"]
        },
        {
          payloadValue: '{"state": "OFF-PEAK"}',
          mqttNotiCmd: ["Command OFF-PEAK"]
        },
        {
          payloadValue: '{"state": "NIGHT"}',
          mqttNotiCmd: ["Command NIGHT"]
        },
      ],
    },
  ];
var mqttNotiCommands = [
    {
      commandId: "Command PEAK",
      notiID: "ENERGY_TARRIF",
      notiPayload: {action: 'PEAK'}
    },
    {
      commandId: "Command OFF-PEAK",
      notiID: "ENERGY_TARRIF",
      notiPayload: {action: 'OFF-PEAK'}
    },
    {
      commandId: "Command NIGHT",
      notiID: "ENERGY_TARRIF",
      notiPayload: {action: 'NIGHT'}
    },  
  ];

  module.exports = { mqttHook,  mqttNotiCommands};

So ‘magicmirror/tarrif/set’ topic gets set to either PEAK, OFF-PEAK or NIGHT via Home Assistant mqtt publish action, and the above sees this then this sets the notification payload to send.

What I don’t understand is how to display the appropriate .png file using your module. I assume notification: “ENERGY_TARRIF” relates to the notification ID in the dictionary (?) but what relates to the payload? Based on your example I assumed it would be, eg: value: “PEAK” with the valueImgIcon underneath but that doesn’t work.

I just get all 3 images showing with NA underneath.

The basic idea of the module is to display values send by notifications of other modules
BUT
the module has the ability to display a default value (naValue) if no value has been send by any other module. It has abilities to display icons instead the value and change the icons based on thresholds (conditions). In combination with the support to define functions to format the values before the check of the conditions it will be possible to get the current time:

{
	module: "MMM-ValuesByNotification",
	position: "top_left",
	header: "Energy",
	config: {
		updateInterval: 60,
		valuePositions: "i",
		valueNaPositions: "i",
		itemPositions: "e",
		groupPositions: "e",
		formatNaValue: true,
		transformerFunctions: {
			naToImgIdent: (value) => {
				let curHour = new Date().getHours();
				if ((curHour >= 0) && (curHour <= 6)){
					//From 0 to 6 o clock
					return "a"
				} else if ((curHour >= 7) && (curHour <= 12)) {
					//From 7 to 12 o clock
					return "b"
				}  else if ((curHour >= 13) && (curHour <= 18)) {
					//From 13 to 18 o clock
					return "c"
				} else {
					//From 19 to 23 o clock
					return "d" 
				}
			}
		},
		groups: [
			{
				items: [
					{
						notification: "ICON_DUMMY_ABC",
						valueImgIcon: "modules/MMM-ValuesByNotification/icons/tom.jpg",
						values: [
							{
								valueTransformers: ["naToImgIdent"],
								thresholds: [
									{
										type: "eq",
										value: "a",
										valueImgIcon: "modules/MMM-ValuesByNotification/icons/tom.jpg",
									},
									{
										type: "eq",
										value: "b",
										valueImgIcon: "modules/MMM-ValuesByNotification/icons/tom2.jpg",
									},
									{
										type: "eq",
										value: "c",
										valueImgIcon: "modules/MMM-ValuesByNotification/icons/tom.jpg",
									},
									{
										type: "eq",
										value: "d",
										valueImgIcon: "modules/MMM-ValuesByNotification/icons/tom2.jpg",
									},
								]
							},
						]
					},
				]
			},
		]
	},
},

Edit:
I should have read your question in detail first :-)
If you can provide the state via MQTT already you can for sure use this module. You will need MMM-MQTTbridge to send the value as payload of a notification. Check for the notification in MMM-ValuesByNotification and display the icon you like.