[web] Split modal into multiple components

Summary:
Manage links modal is complicated so it makes sense to split it into multiple components. Following diffs will introduce new components that are conditionally displayed.

Depends on D8413

Test Plan: This is only a refactoring. Tested if the modal still works.

Reviewers: kamil, inka, bartek

Reviewed By: inka

Subscribers: ashoat

Differential Revision: https://phab.comm.dev/D8414