[web] Migrate drafts to db for everyone

Summary:
Part of ENG-4844
Depends on D9109

We need to migrate drafts for all users to the db.

Test Plan:
Tested on chromium:

• [on master] Replaced code in isSQLiteSupported:

return false; // <- added
if (!isDev && (!currentLoggedInUserID || !isStaff(currentLoggedInUserID))) {
  return false;
}

• logged in, made sure that there is persist:root in local storage, created a draft, closed the web page
• [Applied this diff] opened the web page, and checked if the draft are still there

Reviewers: kamil, inka, atul, tomek

Reviewed By: kamil

Subscribers: ashoat

Differential Revision: https://phab.comm.dev/D9110