Yes redundantly encoding type everywhere in your id will be easier for a specific kind of bug yet you're adding that overhead all the time in both your db mapper and extra bytes everywhere.

Or we are getting reports of invalid order ID let me run a scan across db's and see if its valid anywhere, oh hey it shows up in persons somebody mixed them up somewhere or no it's just invalid somebody messed up in some other way.

If it happens enough to encode it everywhere in ID's you could just have a dev tool that looks for it across your db's with a copy paste, a little longer to scan, vs overhead always in the running app so you can quickly determine that one specific bugs cause. Either way its an invalid ID and being a UUID it won't collide and cause worse problems with overlapping person and order ID as would occur with integers.

I just don't see the value but hey at least you're not storing it that way in the db right?