The web installer expects that the LoadExtensionSchemaUpdates hook handler is an old-style hook that is self-contained, all it does is load that hook and run it without any other parts of the extension.
I noticed this while reviewing https://gerrit.wikimedia.org/r/c/mediawiki/extensions/OAuthRateLimiter/+/613282 in which the hook can't be called without invoking the OAuthRateLimiterTierManager service, except that won't be loaded in the web installer.
Because this system is rather fragile and I want to replace it (T258852: Replace LoadExtensionSchemaUpdates hook with static data in extension.json), I would suggest we don't allow the LoadExtensionSchemaUpdates hook to be used in the new system. Or it would need to be done in a way that doesn't have any service dependencies.
codesearch says so far only Wikibase is using it, and well, Wikibase isn't compatible with the web installer anyways.