Accessing Gmail Password from Android Device Remotely

I was using a Nokia 5 and I lost it over the weekend. I have the gmail app stored there that has sign ins to 3 of my emails s*****@gmail.com, r******@gmail.com & r1*****@gmail.com Unfortunately I have no access to the last mailing address because apparently I forgot the password. It was a fairly new account so when I try to recover the password, google cannot verify its my account. The account is linked to my local bitcoins account therefore I cannot log in and have access to my bitcoins. I have the following question, if I get a new phone and restore android, will the gmail app appear with the accounts logged on? and if not, is there a way for me to find out the password? I am not sure if this is allowed but I will spare some few bitcoins to the person who can help out.( if not allowed, I will edit and remove this part)