[CP][beta channel] Fix null-safety type bug in HTTP code

[lrhn]

commit(s) to merge: 9cbed61

merge instructions: clean merge

What is the issue: Fix null-safety type bug in HTTP code. Triggers if passing a timeout.

What is the fix: Refactor the code to avoid using null as a signal that a timeout happened. Catch TimeoutException instead.

Why cherrypick: It's a bug that prevents all use of the timeout parameter. It was introduced in null safety migration.

Risk: Very little to none. The fix should not change the behavior of any existing code, except where it would otherwise hit the bug.

Link to original issue(s): #44989

/cc @kevmoo @mit-mit @whesse @athomas @vsmenon @franklinyow

[vsmenon]

lgtm