Let's start with what your M1 mini does support. From the Apple specs for this desktop computer:
Video Support
- Simultaneously supports up to two displays:
- One display with up to 6K resolution at 60Hz connected via Thunderbolt and one display with up to 4K resolution at 60Hz connected via HDMI 2.0
- Thunderbolt 3 digital video output supports
- Native DisplayPort output over USB‑C
- Thunderbolt 2, DVI, and VGA output supported using adapters (sold separately)
- HDMI 2.0 display video output
- Support for one display with up to 4K resolution at 60Hz
- DVI output using HDMI to DVI Adapter (sold separately)
The 27" Thunderbolt display supports Thunderbolt. The Apple specs for this display does not specifically call out whether it is version 1 or 2. Physically, either uses a mini DisplayPort.