Been reading other sources in preparation for attempt to connect a TB-2/HDMI 1.4 monitor to a M2Pro 14" in a few weeks. On the HDMI side, some claim that using cables under 1 meter or over 2 meters can be problematic, especially with "Amazon special" type cables. For the over 2 meter lengths, you may need a hybrid optical cable or a HDMI cable with USB power (especially at high rates). On the TB-3/4 side, be careful of supported refresh rates.
Will try the HDMI route first, at macOS 13.2. May be simpler with M2Pro, since M2* uses a non-Intel USB/TB chip. The M1* units still use a Intel USB/TB chip. Mactracker application implies that M1Pro/M1Max supports a maximum of 60Hz refresh rate (but I've seen this free application differ from other sources in the past). I understand the maximum supported refresh rate on the M2* HDMI port is higher than on the M1* models. May also be true for TB4.
Looks like over 60Hz refresh rates are only supported on M1* with ProMotion (and only at 120Hz on the internal display). My older Lenovo 24" should fall well under the 60Hz refresh rate, and has a maximum resolution around 2560 x 1600 or so, if I remember correctly. Attaching link to M1* 14" specifications (Apple).
support.apple.com
If using a newer monitor, and use of a TB-4 port was desired, I'd be sure to use Intel certified TB4 cables from Caldigit, OWC or another manufacturer, not the half-price ones from unknown manufacturers on Amazon. Cable quality will only become more of an issue as newer standards become available. (Will likely junk all USB-2 and USB-3 items after transition to M2Pro, to prevent any mistaken use, also, that stuff is approaching its 10th birthday.)