How to recover Gmail and update Yahoo phone number on Apple Mail for iPhone 15 Max Pro?

My boyfriend traded in his old iPhone for an iPhone 15 Max Pro (I'll call "i15") but didn't have his password for Gmail (aka "G****") to populate the mailbox. Since the upgrade, both Gma*** and his Yahoo mailbox are empty on his MacBook Pro 13 version 17.1 ("MB"). Gm*** is also empty on his i15, but Yahoo is ok. I was able to update his phone number for Gm**** (since it was used on my PC). We still need to update his phone number for Yahoo, which is only accessible on his i15, to make sure he doesn't lose access.

Question 1a. How do we login to Gm*** from Apple Mail on his iPhone 15 Max Pro? I assume we should do this first.

1b. How do we do the same for Yahoo to update the phone number (we don't have access to the one associated with the account, anymore)?

He has a second (unused) Gmail account (aka "Gma***), that's only on his MacBook. Email sent from Apple Mail, is from Gmail173. A reply goes to both Gma** and Gmail1**

Clicking "New mail" on the MB only pulls for Gm***. Rebuild did nothing. (Btw, we don't know the pw for Gmail173. So, it's not an option to use elsewhere).

Question 2. Once we have access to Gmail on his phone (doing this before Yahoo to insure he has at least one accessible mailbox on his phone), how do we repopulate it to his MacBook (within Apple Mail)?

(Question 3. If not the same procedure, how do we get Yahoo back up on his MB?)

I was thinking that we should do Gma*** on his phone, first, since we have a way to recover it. Is there a better order to do all this to regain access to both accounts based on the info provided (since his Yahoo account is still associated to his old phone number)?

My bf does not have much patience to go through lots of steps (which is why I'm doing it) and he's usually using his phone. So, I need to get this accomplished relatively quickly.

Thank you in advance for your help.

[Edited by Moderator]