Please try build 24179 or newer. @ikeblaster made an attempt to fix Skype login.
I'm with SkypeWeb.dll v.0.95.13.3 [30 Aug 2021 11:08:16] - Skype protocol (Web) on MirandaNG 0.96.1 alpha build #24181 (dc4d1cd2f2) x64 and still can't login.
Ultimately getting this in the server response:
"We can't sign you in
Your browser is currently set to block cookies. You need to allow cookies to use this service."
I'm happy to share more info if that can help fix it.