I was working with a colleague of mine the other day on this issue. If you are using WIndows Server 2022 with IIS to setup a website that will use client certificate authentication and notice that you are not prompted for a certificate….. the issue is probably TLS 1.3.
Windows Server 2022 IIS by default uses TLS 1.3. If you check the box to disable TLS 1.3 which will fall back to TLS 1.2 everything works.
Still not sure at this moment who is to blame, Microsoft, or the web browsers.
EDIT: Update from the Microsoft Article
Yes, I got answer: Microsoft implemented TLS 1.3 in most secure way by RFC. IIS wants to perform post-handshake authentication. Unfortunately common browsers do not support it in default configuration. You can enable it only with Firefox (when I last checked, maybe samething changed in near past). So, de facto IIS default configuration for two-way SSL with common browsers do not work with IIS when TLS 1.3 only is enabled.
You can enable IIS and TLS 1.3 only configuration by enabling in-handshake method for IIS instead on post-handshake method.