Has anyone created a field with an own search function in it other than netsuite's own or have any ideas in a good way on how to do it? A suitelet would also be possible of course but the best would be to have the search directly on the record and the field itself (like standard but with some more filtering).

You can use the results of a saved search to dynamically populate a custom field on a record. If your looking for a way to input something to search for, it's going to have to be a suitelet of some sort. https://docs.oracle.com/en/cloud/saas/netsuite/ns-online-help/section_3746191995.html#Creating-Custom-Fields-with-V[…]ed-from-Summary-Search-Results

One thing to keep in mind...I don't believe the field will be available in a saved search though due to it running its own search kind of like source from a sourced field displays in the UI but you can't get it from a search. So if analytics are involved w/ the field I would double check.