A user just posted this question in our chat channel and I'm posting the question here, because I'm interested in the topic and leaving a record of the discussion for future me (who will be dealing with this problem in the next few months).
I did several projects in Drupal 7, using Entity Registration, Node Registration and custom code. Backdrop CMS does not seem to have any of those modules ported... but on the other side, I have the impression that this function is being taken out of any CMS in the long term.
just seconding the suggestion of CiviCRM, its event registration features are very robust.
If you need any help getting it setup so you can experiment with it, let me know