Can I use my old monitor with a new 2023 M2 Desktop Mac Pro?

Without a look at the specs for that display, try it.

Monitors usually swap fine, though sometimes adapters can be required, or a different cable, and some cable and connection configurations won’t play DRM-protected content.

If you want us to look at it, you’ll need to post the particular Asus monitor model.

Asus 27” PLS PB278Q has HDMI 1.4 and has DisplayPort, and should work with either HDMI, or with a Thunderbolt USB-C to DisplayPort adapter and a DisplayPort cable. OWC / MacSales and Monoprice both seem to have an adapter, but you can check with them for details. Monoprice also has a USB-C to DisplayPort cable that should work here.

Apple’s Mac Pro tech specs lack the HDMI standard details, unfortunately. Based on other sources, both HDMI ports are each able to output one at 8K60 or one at 4K120, so two HDMI 2.1 ports.

Easiest and immediately-likely-to-work cabling is likely an HDMI 8K cable. Lower-spec HDMI will work too if you already have it, but I wouldn’t buy a lower-spec HDMI cable nowadays.

As for the display differences, you might not want to ask that question, or might not want to go look at a Studio Display, and might want to continue to enjoy your current monitor. I really didn't understand the differences between what I had been using and an LG OLED until I saw the black levels on the LG, for instance. In the specs for the two monitors, 2560 x 1440 and 300 nits, versus 5120 x 2880 and 600 nits, 12MP Ultra Wide camera, much better speakers with spatial audio, native Thunderbolt display (no adapters), and three USB-C ports.

FYI: I am using a 2017 Asus 28” 4K monitor on my 14” Macbook Pro with the M1 Pro CPU chip, connected via a CalDigit TS3 Thunderbolt 3 dock via a DisplayPort cable. Initially I used a USB-C to HDMI cable, so it works both ways via the CalDigit dock.

There is a very good chance that you can.

In addition to what MrHoffman has offered, have a look at > Connect a display to Mac Pro - Apple Support