using older imac as display for macbook pro m2 Max

That setup is no longer supported by Apple. The iMac cannot be used as a monitor for any of the newest Macs and Target Display mode is no longer a feature of macOS, having been deprecated several years ago.

Please see: Use your iMac as a display with target display mode - Apple Support

Per the link above:

• Your target iMac (monitor) must be using macOS High Sierra 10.13.6 or earlier. 

• In all cases the source Mac that you're connecting FROM must have been introduced in 2019 or earlier and have macOS 10.15 Catalina or earlier installed.

You might consider a third-party solution - Luna Display or Duet Display - though I can’t speak for the performance of those. Regardless, you still will need a proper monitor to set up either of those options.

❝Like any product, Luna Display does have limitations and it’s not recommended for high motion content. For example I wouldn’t recommend using Luna Display for gaming or video editing.❞ - Luna Display website

Do yourself a favor, avoid the headache and just budget an extra $100 for a monitor. Yes, they are that inexpensive.

You cannot, both machines are too new for Target Display Mode, please refer to Target Display Mode. There are software solutions available such as Luna Display however it is wiser to use an external display. There are many available on Amazon that start at less than $100. Whey go this route, simple:

• Simple to setup
• No maintenance needed
• Best performance
• Dead reliable.

rkaufmann87 wrote:

You cannot, both machines are too new for Target Display Mode, please refer to Target Display Mode• .

The 2013 iMac supports Target Display Mode, using Thunderbolt input.

It is the restrictions that Apple added on the other machine – that it must be a Mac introduced in 2019 or earlier, running Catalina or earlier, that would keep Target Display Mode from working for the OP. The M2 Max MacBook Pro is too new to satisfy those restrictions, and does not support using any iMac as a Target Display.