TRRS in its proper glory as a combo headphones and mic connector will provide stereo headphones and mono mic. It may be working on your desktop because you're plugging TRRS into a TRS jack.

It's really a tossup how laptops implement their multi-function capabilities on that single connector. But it is likely a TRRS jack, and things are lining up differently than you expect.

On my Dell Latitude, it asks what device you plugged in when you connect something to the jack. That may give stereo mic functionality, but I've never tried it. I would expect that it would want to see a TRS plug configuration at that point for it to work properly.

If you want to eliminate the guesswork, a dual channel USB audio interface plus a cable that splits the TRRS out to individual connectors for the mics is your best bet. You may get slight improvements in audio quality as well since those onboard connections can be a bit noisy.