Does deleting a property from Google Search Console delete it just from my own list or does it delete it for all users?
It depends on who gave access to the other users. If you delete the property and you are the verified owner that gave access, then everyone under you will lose the access. This means delegated owner as well as users.
However, other verified owners (new or existing) will be able to see every user and re-grant access.
If the verified owner of your site leaves, or you're not sure who the verified owner is, simply verify another owner for your site. The new owner will be able to see the list of all owners and users verified to that site, as well as the method used to verify each owner. You can then optionally unverify previous owners by removing their verification token (for example, removing the HTML tag from the site, for HTML-tag-verified owners).
Source: Google Search Console Help