Hello,
As far as I am aware HDMI cannot be converted to Thunderbolt but you could use your USB-C port with a Thunderbolt 2 converter (assuming the display is using Thunderbolt 2).
MacBook Pro (16-inch, 2021) - Technical Specifications
"Video Support
Simultaneously supports full native resolution on the built-in display at 1 billion colors and:
- Up to two external displays with up to 6K resolution at 60Hz at over a billion colors (M1 Pro) or
- Up to three external displays with up to 6K resolution and one external display with up to 4K resolution at 60Hz at over a billion colors (M1 Max)
Thunderbolt 4 digital video output
- Native DisplayPort output over USB‑C
- VGA, HDMI, DVI, and Thunderbolt 2 output supported using adapters (sold separately)
HDMI digital video output
- Support for one display with up to 4K resolution at 60Hz
- DVI output using HDMI to DVI Adapter (sold separately)"
Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter
I hope this helps.