I’d assume that it would be by whatever the community ID is.
If I couldn’t find it because of a difference in community vs personal ID I’d filter by genus rather than specific species.
Having the map view would also help in cases like this. When you’re first making an ID on someone’s observation you see where it is on the map, but as it currently stands when you go looking for one of your past IDs you don’t see them on the map, so you don’t have that as a memory assist. Being able to see your past identifications on the map would make it much easier to quickly sort through/overcome these types of issues.