https://gerrit.wikimedia.org/r/c/operations/mediawiki-config/+/966798 will remove the sole caller of EnterMobileMode (as far as codesearch can tell). After that, we might want to consider whether the hook is still useful.
Historically there were a couple non-CentralAuth-related uses ({355a2710231f27cf162f3ba01b2e90c122aea266} for CentralNotice, {fd885d988112517f691df6da43089af2c8c7862e} for UniversalLanguageSelector, the never merged {aec20bade127ca88ab4c73f2c9f1b0224da88a40} for NavigationTiming) but those didn't survive.
The hook was added in {c5228db3de9877436349fa65291524f4e47c2dcb} to "inform other extensions that we're going to have a mobile page view"; that use case makes sense, but the hook doesn't serve it well, because it's called at an unpredictable point in time, leading to issues like {f8ad56ce4d8ab4d9e790155fd1263d2dae9e72c7}. I think it would be better to just expose `MobileContext::shouldDisplayMobileViewInternal()` and internalize `setForceMobileView()`, which only has a single caller.