After the update to v0.60.55 (release), Twitter web notifications no longer function in Brave. This is not strictly because they don't function - but rather because they can't be set from within your Twitter profile settings.
Profile --> Settings & Privacy --> Web NotificationsTurn on to enable web notifications for TwitterAllow in browser modal - do so.
After clicking allow, the page refreshes and changes are not saved. Notifications are not enabled and the page looks as if you had just arrived there, but now the Turn on button is unresponsive.
Web notifications should be enabled.
Always
Current release: Yes - v0.60.55
Dev/Beta builds: Yes - v0.62.6/v0.61.36
Initial user report was very detailed and well written, found here. I also attached short recording of the behavior.
https://community.brave.com/t/unable-to-turn-on-twitter-web-notifications/45690/3

I did a Safeboot with Networking and only opened Brave, not Firefox. Same problem with Twitter notifications.
@Brave-Matt is this still an issue?
@bbondy @rebron
Just tested on v0.61.51 and it is still an issue - in fact, the option to click the "web notifications" button is no longer present and now displays the following message:

Still an issue in the new Twitter UI. It will ask for permission, however the "switch" (see screen) stays off and the animation seems broken.

Worth noting that this issue exists even when the Brave and Rewards extensions are disabled:
> brave.com --disable-brave-extension --disable-brave-rewards-extension
Likely a duplicate of https://github.com/brave/brave-browser/issues/2301
I'm curious if Twitter is trying to push a message and making sure you acknowledge it before enabling (or browser would prompt you first time, "allow notifications from x?")
+1 User mentions that this has caused them to revert back to Chrome. https://www.reddit.com/r/BATProject/comments/dnay4q/when_will_the_twitter_notifications_bug_be_fixed/f59b6mk/?context=3
Still an issue +1 :
https://community.brave.com/t/unable-to-activate-browser-notifications/94142/4
Still an issue, yes. When I click on "enable push notifications" I'll get informed that my browser won't support push-notifications.
Here's a screenie of the result:

Issue not resolved as a side effect of other updates. Gonna need specific attention.
Closing as a duplicate of https://github.com/brave/brave-browser/issues/2362
Most helpful comment
@Brave-Matt is this still an issue?