I don’t think you can add scripts into an app itself. I don’t think setting a formula from within the app would work either, as google may only see it as text instead of a formula.
The only option I can think of while in Add/Edit mode would be to use a Form Button to submit your search term to a new sheet. Then use a formula to pull the last submitted search term into the cell that you are using to filter your choice list. I would think this would update the Choice component while your are still in the Add/Edit mode, but may take a few seconds to update. It wouldn’t be a very smooth process, but may be something to try.