Is anyone having issues with accessing the VPN, Teams, Outlook, after getting a new CAC?

I had the same problem, especially with VPN access, after updating my credentials. It was really frustrating because everything seemed fine with my certs, and I went through the whole recovery process, but nothing worked. I tried all sorts of troubleshooting, thinking it might be an issue with the new certs not being properly recognized. What finally helped me get around the issue wasn't another round of certificate recovery but switching to a proxy for my connections. I found a Netherlands proxy list online and decided to give "HollandProxy" a try. Switching to this proxy surprisingly resolved my access issues to VPN, Teams, and Outlook. It felt like a workaround, but it got me back on track with my work without further hiccups. You can see the list here: https://cyber-gateway.net/get-proxy/proxy-by-country.

For CAC related issues on non-Government computer's I always refer to:
https://militarycac.com/

Did you go talk to your S6? I had an issue when I got a new CAC in July I couldn't get my digital signature to pull up even at work. It just said "no card found" and the 6 installed something that fixed it. I can't remember what. I had issues before that even on the VPN when I worked from home and since they installed whatever they did, I have no issues if I have to work from home when my kid is sick or something.