I believe a Regular can edit a topic title indefinitely while they remain a Regular.
There is a small delay between achieving the Regular badge and it appearing on your usercard, which would explain the first screenshot in the OP. However you get the perks straight away even if it’s not quite reflected in your usercard yet, so that shouldn’t be an issue.
Admins and Mods do have the ability to ‘edit lock’ individual posts from the post wrench, which would also block title edits if done on an OP. It pops a little padlock icon on the post, but it’s only visible to staff and the user whose post it is.
@S_B_2_Go You may need to ask the admin of that forum if there is anything special about that topic.