Fixes #5657.

### Description

Enable config to also type check untyped functions (not in tests).
- Type annotations were added
- Explicit casts were added
- Variable redefinitions with other types were refactored 
- If no other option was available (or it would be overly verbose) `#
type: ignore` was added

### Types of changes
<!--- Put an `x` in all the boxes that apply, and remove the not
applicable items -->
- [x] Non-breaking change (fix or new feature that would not break
existing functionality).
- [ ] Breaking change (fix or new feature that would cause existing
functionality to change).
- [ ] New tests added to cover the changes.
- [x] Integration tests passed locally by running `./runtests.sh -f -u
--net --coverage`.
- [ ] Quick tests passed locally by running `./runtests.sh --quick
--unittests --disttests`.
- [ ] In-line docstrings updated.
- [ ] Documentation updated, tested `make html` command in the `docs/`
folder.

Signed-off-by: Felix Schnabel <f.schnabel@tum.de>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>