Softr Support (Viktoria is amazing) was able to help me with my issue. Hidden fields like {URL_PARAM:recordId} do not get recognized by Make using ‘Click here to send test data’ in Softr Studio. I had to actually published my app first and send data from the live app in order for Make to recognize it.
I think it can be good idea to include a hint that some data structures is not synced with unless the app is live. I suspected there was some issue with data strucutre synchronization after some fields of mine showed on Make and others don’t when there seem to be no reason for it to be different than other fields.