We had the same issue and could narrow it down: It's because of a new Chromium feature TLS 1.3 hybridized Kyber support starting from Version 124, which breaks TLSv1.2 Handshake. In our case, we also had the problem, that we cannot connect with a Browser to our Cisco ASA outside address with the Error ERR_SSL_PROTOCOL error with Chrome and Edge (nevertheless it works with Firefox, Safari, etc. which are not using Chromium).

You can change back this behavior with the Chrome / Edge flag

chrome://flags/#enable-tls13-kyber
respectivley
edge://flags/#enable-tls13-kyber
Set this to disabled. After this the connection with the browser works again.

However, this doesn't solve the problem with Anyconnect connection because Anyconnect uses Webview2 Runtime, which doesn't use the flag set prior. To workaround this problem you have to create the following DWORD registry value: Computer\HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Cisco\Cisco AnyConnect Secure Mobility Client\UseLegacyEmbeddedBrowser with value 1. This tells Anyconnect to use the Legacy Browser (IE) instead of Edge and the connection works again.