If an answer-banned user tries to use the contact form, they are supposed to select "My question or answer was denied". Doing so brings up text that speaks exclusively of question bans:
Users who are banned from asking questions see the following error message when trying to post a new question:
We are no longer accepting questions from this account. See the Help Center to learn more. Stack Exchange cannot lift question bans by request.
The only way to end a posting ban is to positively contribute to the site; automatic bans never expire or “time out“. Visit our help page for more details.
There is a link there at the very end of "question bans" page, but why would one read the entire text of "question bans" if that is not their problem?