What to do with tuf/exceptions before 1.0.0?

Description of issue or feature request:

Currently, we are using tuf/exceptions.py to store client and repository exceptions both for the new and old implementation. After we drop the old code we will have to keep the exceptions from tuf/exceptions.py or move them to somewhere else. Some of the options I and @jku come up with are the following:

1. create a new exceptions file in tuf/api/exceptions.py storing all exceptions needed from the client, metadata API, and future repository code (see #17256). Then when the old code is dropped the tuf/exceptons.py will be removed as well.
2. keep tuf/exceptions.py and just remove the old exceptions.py after we remove the old code. This will require linting the file and changing the docstrinsg (see https://github.com/theupdateframework/python-tuf/pull/1721)
3. create new exceptions files: one in tuf/api/ with repository side and metadata API exceptions and one in tuf/ngclient/ where we will store the exceptions for the ngclient. Remove tuf/exceptions.py together with the rest of the old code.

Option 1 or 2 seem easier to change with less code, but option 3 will provide better encapsulation

[lukpueh]

I think it is more important to figure out which (custom or built-in) exceptions we raise where (see #1131, #1312, #967) than where we define custom exceptions.

[MVrachev]

We have decided in #1725 that we would place the new exception file in tuf/api/exceptions.py, so this issue is solved.