ensure important clients migrated to the new analyzer API

[devoncarew]

todo: identify and list clients

• kythe (Migrate Kythe support to the new analyzer API #31645)

/cc @scheglov @bwilkerson

[jmesserly]

FYI, I made #35013 for moving DDC off task model

[natebosch]

@devoncarew - can you update the issue or point to some documentation that explains what "Task model" means and what it's replacement is? I'd like to have somewhere to link to when I see code using AnalysisContext.