I have an old 27" Apple Display Model A1316. Is this comparable with the M2 Max Studio?

Not exactly.

LED Cinema Display (27-inch) - Technical Specifications

is the full list of specs. If you want to know how that differs from the more modern display or don't understand a technical term please ask what you need to know.

Some of these displays use Dual-Link connectors. Be sure if yours does, the adapter you use is one that has it. Otherwise you might only get video access over the cable, or limited resolutions.