Is there any way that a User can reset his/hers password while logged in (by providing the current password)?

Not unless you role your own functions to check and change the password with an rpc call. There is work in gotrue to allow password change with a code sent to the users email. Some discussion on password reset: https://github.com/supabase/gotrue/pull/309

hmmm I see. I am using the js client. So weird this is not there. Its pretty important