JS Alert completion - Investigate usage in the ShareSheetCoordinator

[data-sync-user]

Follow up to the work regarding the touchy JS alert completion handling in https://mozilla-hub.atlassian.net/browse/FXIOS-10334

Please see this screenshot and the corresponding FIXME note in the code for FXIOS-10334:

!Screenshot 2025-01-10 at 10.37.36 AM.png|width=3222,height=1594,alt="Screenshot 2025-01-10 at 10.37.36 AM.png"!

// FIXME: FXIOS-10334 It's mysterious that we are calling dequeueNotShownJSAlert in the share coordinator. It may not
// be necessary, but this JS alert code is fragile right now so let's not touch it until FXIOS-10334 is underway.

We need to evaluate whether we should still be trying to call dequeueNotShownJSAlert from within the ShareSheetCoordinator.

[~accountid:616d884c5800630069ebf285] suggested that while the reason is unclear (and there may no longer be one), we should wait until the https://mozilla-hub.atlassian.net/browse/FXIOS-10334 fix is validated in prod and then investigate this area of the code. Apparently Brave does something similar regarding share sheets.

┆Issue is synchronized with this Jira Spike