You have always been on Yahoo, there was a migration to BT Mail but that stopped about 3 years ago. You should always use 'other' regardless of which system you are on.
Once again, sorry to butt in.......It’s subtle. All settings are correct, as given, but there’s one extra task.
In the main account settings screen tap on the smpt tab, “mail.btinternet.com”.
Tap on Primaryy Server, select. Then make sure you write in your new password, over the dots which hold your old password.
Just done it on my old iPod iOS 5.1.1., which has been idle for a few weeks. Account is verified.
Hope this helps, rather than adding more confusion. You will get there, eventually.
Maybe it just doessn't work with iOS 9.
Having established that BT have shuved one of it's first members (me) into Yahoo - the one that got itself hacked, I have tried to use the settings given in your links above for a Yahoo setup. This includes overtyping my password for incoming and outgoing mail servers. The link shows IMAP and SMPT included before the mail.yahoo.com which I believe should not be included on iOS setups but I tried both anyway.
Nothing seems to work in connecting me to Yahoo on my iPad. At least when I used the BT setup I could connect. Just couldn't send. There are no stuck emails in the Outbox on my mobile devices.
Is this the problem? https://9to5mac.com/2018/02/20/yahoo-email-not-working-with-iphone-and-ipad/
You were not "shuved" on to Yahoo. You have always been on BTYahoo!
I would suggest that you delete your email account from your device then re start your device and once it has restarted set the account up again.
Set it up manually using the BT server settings entering your details and password manually to both servers.
Ok I deleted the account and restarted. Adding other account I was asked to enter username and passwords for incoming and outgoing servers. Up until this point I have always been asked for one server's details and that is when it was working and not working. It didn't recognise them to I re entered. Then I got all the ticks for the very first time and it recognised my account details for once.
It still wouldn't send though getting stuck in outbox. Shortly after that a box came up saying my account details have not been recognised. Frustrating. Very frustrating.
From my ipad that is. Never a problem sending with Android and PC. The trouble seemed to start soon after fighting with an android to connect it. Perhaps a load of different passwords were stuck on the Yahoo server cache.
Just to top off then the solution for my iOS 9.0 device was to delete the account but you must restart the device and then add the account choosing Other. Instead of being asked to give a password for one server (and it has done for years) after the restart I was asked to give it for both incoming and outgoing servers this time. I will say the last contrubuter entry put me on the right path by asking me to restart.
Since this happened to all the iOS 9.x devices I handle it's likely either BT, Yahoo, or Apple have made a change for this problem to happen.
Just to top off then the solution for my iOS 9.0 device was to delete the account but you must restart the device and then add the account choosing Other.
As detailed in the link I posted in message 7 of this thread a week ago.