Why won't my Mac running Sonoma prompt me for my *** certificate on .mil websites?

I cannot get my Mac to prompt me for my *** certificate when I try to access .mil websites. The computer can see my smart card reader and read my certificates. I can sign documents with my *** using Adobe Acrobat. I have tried both of my *** readers that previously worked with my MacBook and neither will work on Chrome or Safari. I went to militarycac.com and restarted the entire process of installing the certificates in my keychain to no avail. I'm not sure if this is a Sonoma problem or something else but I've tried every solution I can find online and nothing has made any difference. Any help would be greatly appreciated.

[Re-Titled by Moderator]