Another workaround that works most of the time is to type something in the chat then backspace till the box is empty then press enter. This is definitely painful since I’ve had to do it a few times.
Has been happening for about a year and a half now. I thought this was completely intentional, but it does appear to be a bug. I was able to type something into the message box and then delete the message and the notification goes away sometimes, but this doesn’t appear to work anymore for me.
Additionally, chat notification sounds do not play when someone sends a private message (it has played the sound in the past for me).
The website chat sound hasn’t existed since they overhauled the chat system in 2018 or so removing the Party feature (which allowed users in a party to automatically join what the party leader is playing; this was therefore a great feature that unfortunately may have been inappropriately abused) and replacing it with a banner for what the friend is playing as well as the game you previously played, so the removal of the sound sadly may have been an intentional but reasonless change when the chat system was redone.
I can confirm this bug has been around since the chat system was introduced.
In fact, for a few years after chat was introduced you had to actually send a message to clear a notification. It’s only in the past few years that typing and then erasing could clear the notification.
Due to it being around for several years now I genuinely believed that it was intentionally that horrible/annoying by design (considering it’s not even close to the first time Roblox has made a god awful UX, and by far won’t be the last)