However, that doesn't work, and it probably isn't a good solution. How can I do it correctly? Can I use a javascript class in vuex state at all?

Getter

import { ChatMessage } from '~/classes/ChatMessage'

export default {
  getChatMessages: (state) => {
    const messages = _.orderBy(state.messages, 'created_at', 'asc')

    messages.forEach((message, index) => {
      const ChatMessage = new ChatMessage(message, index, messages)
      message.isNewDay = ChatMessage.idNewDay()
    })

    console.log(messages)

    return messages
  },
}

Class file:

export class ChatMessage {
  constructor(message, index, messages) {
    this.message = message
    this.index = index
    this.messages = messages
  }

  get isNewDay() {
    return true
  }
}