How do I use MIT app inventor's background task extension which helps the app to run in background?

[Kumaraswamy]

You cannot use Firebase extension with Itoo, since a procedure will be called in background, the only way to interact with components are with the blocks, and you cannot set "FirebaseToken" by blocks, its hidden. You can try out alternatively by using an firebase extension.

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@Emre_Karci

Likewise, I need to pull data in the background with the airtable, I need to send a notification when the data changes, but I tried every version of the extension, but none of them worked!

I guess you are talking about the Old Background Tasks Extension, that is maintained nomore, you have to use the more reliable Itoo Extension instead.