MacMini M1 and Apple 27" Thunderbolt Display

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.

Yes it works fine.

The Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter works great with my M1 MacBook Air

and my 27" Thunderbolt Display!