[web][native] update InputStateContainer logic for sending text messages

Summary:
ENG-8424.

This makes updates code to use one hook on both platforms which handles both thick and thin threads, and avoids hacking logic on both InputStateContainer implementations.

Depends on D13328

Test Plan:
Tested end-to-end according to the process described here.

Additionally, tested creating threads and sidebars.

Reviewers: tomek, inka

Reviewed By: tomek

Subscribers: ashoat

Differential Revision: https://phab.comm.dev/D13329