I'm not the greatest expert of Shiny, but I would say what you want is possible, but not easy.
By design of Shiny apps (wherever they're hosted), each time someone connects that creates a new session, that independently tracks data in memory. So if you want communication between sessions, you need some kind of mechanism to store the data outside of the app itself.
As far as I can tell, this is not possible on shinyapps.io (independently of the tier), as the "hard drive" that the app sees is re-created independently for each new session. Here is where I get it from:
When going through the different storage type options below, keep in mind that if your Shiny app is hosted on shinyapps.io, you will have to use a remote storage method for the time being.
So you'd need to have some other server where you host the persistent data. For a free and effortless service, I think the easiest is to use Google Sheets, see here for some code. The idea is that you can create a google sheet somewhere with your google account, and have the Shiny app connect to Google and put the data in the sheet. At the end you can have the app recover data from the sheet. Each instance of the Shiny app is not aware of the other instances, but they all put their data in the same sheet.