How do I allow users to edit previous submissions such that appointment dates previously booked are automatically released for other users?

You can allow your users to edit their submission by giving them the EDIT SUBMISSION LINK. The best place to include this link is either through the THANK YOU PAGE or the AUTORESPONDER EMAIL they receive after submitting your form.

Complete guide: How-to-Let-Users-Update-Their-Form-Submissions-at-a-Later-Date

If your goal is to do this for people who "already submitted" your form though, then you can also edit the submissions on their behalf.

Related guide: How-to-Edit-Submissions-Made-on-Your-Forms

You coined the phrase "automatically released for other users". This only applies if you're using a widget that tracks submissions (e.g. the Inventory Widget). However, when I checked the last form you edited https://www.jotform.com/83184288776170 it appears this booking form doesn't actually have a way to reserve appointment dates. It's just asking for departure and return time using the regular date picker field.

In case you're working on a different form, please don't forget to share the FORM URL with us the first time so we know which form you're working on.