Ideating how to send notifications for chat rooms?

Question

We provide different chat channels for users to talk about various topics.

Every user has access to the chat channels. Here is the code for a channel:

constructor(props) {
    super(props)
    this.state = {
        messages: [],
        currentUser: null,
        isLoading: true,
        messageID: "",
        isTyping: false,
        messageText: "",
        roomName: this.props.route.params.roomName,
    }
}
//---------------------------------------------------------------
async componentDidMount (){

    **Code to get current messages**
    
}

//Add a message to firestore
onSend = async(message) => {

    this.setState({isTyping: true,})

    const messageID = uuidv4()

    await Firebase.firestore()
    .collection("chatRooms")
    .doc(this.state.roomName)
    .collection("messages")
    .doc(messageID)
    .set({
        _id: messageID,
        text: message[0].text,
        createdAt: new Date(message[0].createdAt),
        user: {
            _id: this.state.currentUser.id,
            name: this.state.currentUser.name,
            avatar: this.state.currentUser.avatar,
        },
        
    })

     Analytics.logEvent(`ChatMessageSent_${this.state.roomName}`)

}

Now, when a user sends a message in any channel, I want to send a notification to all users who have push notifications on that there is a new message in xyz channel.

My thoughts are to do this in onSend():

When a user sends a new message, call a firebase function to send a notification to all users that there is a new message in xyz channel.

I can't think of another way to do this. I already know how to send push notifications, how to change a tab bar icon if there are notifications, ETC, but am having trouble ideating how exactly to go about this since there are multiple channels.

I am also worried that these notifications will be too "spammy". Perhaps sending out notifications if they have x amount of unread messages across all channels?

Let me know if you have a better idea, thanks in advance.