But we’re not seeing some screen sharing of the android app
We're getting into weeds and details of what is remote and approaching the grey line of question of ownership in online software, services and games. Fact of the matter is, thing didn't work without a phone for 13 years. Or if a phone is not Android or iOS. Or if a phone is dead. Or if you left your phone at car or at home. Or if a phone has broken camera. Or if it's out of service. Or if the app has been killed by power or memory optimizer. Or so on and so forth, which is already a terrible UX worthy of criticism.
It’s not stored on any server
It is stored as an encrypted blob on your gdrive. It asks you about it on every login. Otherwise, how would you recover your chat history if you lost or changed your phone.
Locking the data onto one device is actually worse in terms of security. Assume someone stole your phone or just found it after you lost it. Additionally, assume that screenlock has been bypassed - most Android devices are very bad in this regard. Now the other person has access to your messenger and you can't even kick them out. Not until you go to the carrier and do the whole recovery rigamarole, and get a replacement phone, assuming you don't actively carry a spare one with an active session with you.