The old application had a purge parameter to clear the template cache. The new application should have a route that does this, otherwise wiki changes are not reflected in the application.
A request from the wiki to the app would be the deluxe version, but would require changes to the ContentStaging extension and make it a bit slower. This task is only about the FundraisingFrontend side.
Cache warming would be nice, however it would need some registry of used templates. Twig only provides a very rudimentary cache interface with no such registry. Implementing this would be a separate project and would bump up the complexity considerably. So I'd like to postpone that until we run into problems.
I'd call it /purge-cache.
For security you could store the date of the last purge somewhere and create a class that uses the MedaiWiki API to get a list of recently changed pages and compare the newest page to the date of the last purge.
The old application did not have any protection except for chekcing for a very short, fixed string (I won't disclose here), so the API-based protection feature might be a separate feature in "New Stuff". To have a least some protection you could check for a secret parameter than can be configured in the config file.