That's pretty common IME though the ones I've driven didn't make decisions based on that.

Last few cars I've rented had a speed limit sign generally matching the speed limit on the dash, and on the one I rented this christmas passing a speed limit sign (or an other sign triggering a speed limit change) while on limiter or cruise control would flash a message suggesting pressing a button twice to change the configured speed to that (rather than manually adjust using the +/- buttons).

They were mediums (C-segment) and compact MPV not large or luxury, which I expect is why the sign reading was mostly to purely indicative.

Yes, many cars do now. Some of the "less smart" cars don't necessarily know which signs are which. My 2018 Accord thought the speed limit was 100mph when I was on Highway 99.