Support running the default homemade engines without the need to provide a `homemade.py` file

[AttackingOrDefending]

Type of pull request:

• [ ] Bug fix
• [x] Feature
• [ ] Other

Description:

This will also allow any custom dockers built with a changed extra_game_handlers.py file to work without needing to change lib/extra_game_handlers_wrapper.py.

Related Issues:

https://github.com/lichess-bot-devs/lichess-bot/pull/936#issuecomment-2067743469

Checklist:

• [x] I have read and followed the contribution guidelines.
• [x] I have added necessary documentation (if applicable).
• [x] The changes pass all existing tests.

Screenshots/logs (if applicable):

[MarkZH]

Go ahead and merge this, too, if no more changes are needed.