does mac mini have built in microphone

No the Mac mini does not have a built-in Camera or Microphone.

If the Samsung display has a Camera and Microphone, then you maybe able to use those.

If not, then you need to get and use a USB Web-Cam with Microphone.

I just looked up specs for Minis from 2023 back to 2009 and none show a built-in microphone. Through 2014, they had a 3.5mm audio-in jack, but that disappears in the 2018 models.

Apple - Support - Technical Specifications

I use a Logitech C920 HD webcam with my M2 Mac Mini Pro. The webcam provides an audio source via the attached USB cable to the camera (selectable Sound input) and I have used the camera with Cisco's WebEx, but not Zoom. I do understand some previous posts in the communities showed success with this webcam via Zoom.

I'm unsure if they all do. I think some do. which model year mini are we discussing?