Currently if you search squishy joycon no results point to a bad battery. I’m hopping this will help someone on the future who is confused by a squishy feeling joycon.
This happened to a joycon that sat for a long time and is about 6 years old currently. Squishy is the only way I can describe holding this. Looking at it from the side you can see gaps and bowing which is a huge sign of a bad battery. While attached to the switch I can feel the edge sitting a little abover the switch instead of flesh with the edge. Check your warranty, if you still got a warranty I suggest sending it in for a bettery replacement. If you want to take apart your joycon (voids warranty) and confirm a bad battery you will need a triwing 00 screwdriver and a pick. Watch a disassembly video to avoid damaging a ribbon cable just on the inside. If you can’t quite tell if the battery is bad or not try spinning it on a table. A bad battery will spin and a good one won’t.
That’s it for all the info I got, hope this helps someone.