[web] cleanup manage invite links existing link modal

Summary:
This diff cleans up the one off styles in the manage invite links existing link modal and replaces it with styles of the redesigned modal.

Linear task: https://linear.app/comm/issue/ENG-5943/extendmodify-the-modal-props-api-to-follow-new-modal-designs

Depends on D10238

Test Plan:
Please see screenshot below

Reviewers: atul, rohan, kamil

Reviewed By: rohan

Subscribers: ashoat, tomek

Differential Revision: https://phab.comm.dev/D10239