[web] implement new InlineEngagement design

Summary:
implemented new InlineEngagement design. The new design splits the InlineEngagement into two seperate parts

Depends on D6317 and D6302
Linear Task: ENG-2720

Test Plan:
Please watch the demo video to see the new InlineEngagement

Reviewers: atul, tomek

Reviewed By: atul

Subscribers: ashoat, tomek, atul

Differential Revision: https://phab.comm.dev/D6318