Greasy Fork

No longer works.
Please update it so I will update my rating

Updated for the new html changes. Thanks for reporting. Please update your rating.

Thanks

I am still seeing the signature when I click on "new message"

Please update the script now, I had it as Unlisted (because of this) so updating didn't work, I made it Public again.

Nothing changed

Are you sure? Please check version in the script code manually, it should be 2023.6.1 .
It's working fine for me, with both having custom signature or not. I checked multiple times with both Tampermonkey/Violentmonkey with Chrome, having "Beta Access" on or off.
Remember, Greasemonkey is not supported and it's not working with Firefox (see here).

yes
I use edge and tampermonkey

When I click on the top left "New message" the default signature is still there

It's working fine for me in Edge 113 with Tampermonkey beta, I just checked: https://i.imgur.com/bB71tMv.jpg

weird...

Have you clicked on the red new message button?

Of course. It's working fine even if I click it repeatedly (open multiple composer windows): https://i.imgur.com/4A1baj7.jpg

well that does not work for me but ok

Maybe some other userscript or extension is conflicting with it? I'd suggest trying with a fresh Edge/Chrome profile, with only TM/VM and the script.