Hey zursorzur121,
We'd recommend reviewing this article as it provides information on using an external display with your Mac that may be helpful: Connect one or more external displays with your Mac - Apple Support
"Connect the displays with a cable
For each display, securely connect a video cable (and adapter, if necessary) from a video output port on your Mac to the video input port on the display. See About the video ports.
You can connect one or more external displays, depending on your Mac.
- For Mac computers with the Apple M1 Chip: You can connect a single external display to your Mac. Docks don’t increase the number of displays you can connect. On a Mac mini with M1 chip, you can connect a second display to the HDMI port. See the Apple Support article Mac computers with Apple silicon.
- For Mac computers with Thunderbolt 3 (USB-C): You can connect a single display to each port. If you connect multiple Thunderbolt devices to each other, the Thunderbolt 3 display must be the last device in the chain. If your Thunderbolt 3 display has USB ports, those can be used for data and power.
- For Mac computers with Mini DisplayPort, Thunderbolt, or Thunderbolt 2: You can connect up to two displays. If the displays themselves have Thunderbolt ports, you can connect one display to another, and then connect one of the displays to a Thunderbolt port on your Mac. If your Mac has two Thunderbolt ports, you can connect each display to separate Thunderbolt ports on your Mac. A DisplayPort device must be the last device in a chain of connected Thunderbolt devices. See Connect a display, TV, or projector to Mac.
- For Mac computers with Thunderbolt 4 (USB-C) and HDMI ports: You can connect up to four external displays to your Mac, depending on your Mac model. See the Apple Support article Connect a display to your Mac.
Note: Only the device directly connected to your Mac receives power from the computer’s Thunderbolt port. The other devices in the chain must be powered by separate power adapters."
As your new Mac uses the M1 Chip and your older Mac does not, this could explain why its working on one but not the other.
If you need further assistance with that, we'd recommend contacting Apple Support here: Get Support
Thanks!