Use enableLegacyExtensions over the other feature flag

Created by: philipp-spiess

This is a follow up to #39227

When we merged this PR, we did not have the newer feature flag yet. We want to seperate the option to deprecate the extension system from the option to enable the new integrations as core features. This just makes sure we use the right flag everywhere.

Test plan

I reproduced @vdavid's testing plan from #39227 but did not make screenshots (they look like the one David was posting though 🙈 )

App preview:

• Web
• Storybook

Check out the client app preview documentation to learn more.