Migrate off of deprecated analyzer 10.0 APIs

[scheglov]

I'd like to remove these deprecated APIs in analyzer 11.x

And I have to have drift_dev migrated internally in google3, which is done by rolling external changes.

[simolus3]

I can't fix the deprecation warnings on the main develop branch due to constraints from the latest stable Flutter release. I've created the analyzer10 branch instead and migrated off of deprecated APIs there. Let me know if I've missed anything, otherwise you can mirror that branch for now and I'll ping you here once those changes are on latest-release.