Fix contextually typed object literal completions where the object being edited affects its own inference

[andrewbranch]

This is Wes’s alternative to my PR #36364, which fixes #35702.

[weswigham]

Approve with nits mentioned above, but since I'm a partial author you should get another set of eyes to look over it, too~

[sandersn]

I'm a little leery of the complexity of this change right at the end of the beta.
But @weswigham argues that we remove some scary complexity from contextual typing and push it right to the edge the checker's API.