Move shared test helpers into helper files

Each helper that more than one test file uses moves out of the test file
that holds it into a file without tests, named for what it holds: the
fake Responses endpoint, the fake ChatGPT login service, the fake Bot
API, the terminal test client, the daemon start with a bot, and the tree
node helpers. A helper that only one test file uses stays in that file.
A reader then finds a shared helper from the file name, and a test file
holds only the tests and the helpers of its own feature.

The code of the helpers does not change.

Issue: 947bddb