Share all clicked values(by individual users) of a view with all users who accepted invitation in kotlin/android

I have an app in which all users that accept invitation are stored under one room in firestore cloud.

When the individual users select a value it should be stored in a sliding up view,and that should be seen by all users.I know how to create the slide up view,I just wanted to know what logic or way can I use for this feature

I have explained what I want to do in a rough diagram below.

Is there a way to show all values selected by individual users to all users without using firestore?

First user diagram(selects a value which should go to the slide up view): BEFORE:

AFTER:

Second user (should be able to see value added by first user as well as the value he adds):

BEFORE:

AFTER: