Possible race condition when sharing Supabase client across users

Say I have something like this as a request handler of my server:
async def get_session_middleware(request: web.Request): 
  # Get tokens from cookies       
  await supabase.auth.set_session(access_token, refresh_token)
  user = await supabase.auth.get_user()
  return user

If two users send a request at the same time, is there a chance that one of them will get logged in as another user? What is a better way of handling this?
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