[web] Fix multimedia sending conditions for thick threads

Summary:
Implements 2c from ENG-9345.
Details in the Linear comment.

Depends on D13419

Test Plan:
Successfully sent a photo:

• "quickly" (before upload finished) and "slowly" (waited until preload completes)
• For thick and thin thread

Reviewers: kamil, tomek

Reviewed By: kamil

Subscribers: ashoat

Differential Revision: https://phab.comm.dev/D13420