Add deprecated warnings to TestClient on use of timeout argument

[iudeen]

Implements the solution in #1108 (comment)

Checklist

• I understand that this PR may be closed in case there was no previous discussion. (This doesn't apply to typos!)
• I've added a test for each change that was introduced, and I tried as much as possible to make a single atomic change.
• I've updated the documentation accordingly.

[iudeen]

@lealre I like the way you had created the test! I added that part of it from your PR. 😄