Well, it would mean to add new code to the IDE. And since ctrl-e does not have a checkbox to toggle, it would mean to add a new key-combo.
Such a feature could be contributed...
Reg expression incr search would have interesting side effects though, as the found pos would jump forward and backward.
Imagine you are starting at line 10, and start searching Foo and that is found at line 20.
No you add to your search pattern Foo? and that can be found at line 12. So the search needs to go back...
For now you have some other options...
Once you searched (normal) you can repeat that search. But of course only if you havent searched something else...
You can however create a PascalScript macro
https://wiki.lazarus.freepascal.org/Editor_Macros_PascalScript#FunctionsAnd call searchReplaceEx with a hardcoded search pattern. Then you can assign it to a key, and that key will always do the exact search you gave in your post.