[Sema][NFC] Cleanups after 843cc474 (#87996)

I forgot to tidy up these lines that should've been done in the previous
commit, specifically:

1. Merge two `CodeSynthesisContext`s into one in `CheckTemplateIdType`.
2. Remove some gratuitous `Sema::` specifiers.
3. Rename the parameter `Template` to `Entity` to avoid confusion.