I've just read through the BTYahoo link. It isn't quite what it seems, in three ways

.
First, it isn't "Authentication" as we understand it. In particular, the normal email client authentication setup seems not to be affected. It is a BTYahoo "verification" routine.
Second, the whole thing seems purely to address webmail. It may or may not apply to emails sent from an email client. Unless, reading rapidly, I missed something to do with that.
Third,
You will now be able to send or receive email from the newly verified email account; you'll see the option to choose which email address to send emails from when you compose a new email.
When you check for new emails, all email accounts that have been verified will be checked and the emails delivered to your BT Yahoo! Mail account.
Typical BT Yahoo complication which many years ago was the reason I determined when getting broadband and email at home never to go anywhere near the BT Broadband service. I shall never forget the hidden takeovers in seemingly innocent "Click here to improve your BT Broadband experience" type banners, and finding Yahoo and its garbage, (in those days that was emphatically what it was), had been installed completely screwing up both my email and Explorer Home Page setups, plus adding infuriating irrelevant-to-my-needs toolbars.
My broadband basic info/help site - www.robertos.me.uk
My domains,website and mail hosting - Tsohost.
Internet connection - IDNet Home Starter Fibre.
Live BQM.
"Where talent is a dwarf, self-esteem is a giant." - Jean-Antoine Petit-Senn.