If your HDMI cable and monitor's HDMI versions are of a late enough HDMI version to support your resolution at the 60-Hz level, then I have no reason a Thunderbolt connection to that monitor is going to improve things for you in terms of the monitor serving as a monitor.
But Thunderbolt monitors are often more expensive and at least some have 'hub' functionality. You already have the ports on the back of your M2 Pro Mac Mini, and a Thunderbolt cable to one Thunderbolt monitor. Even if your other Thunderbolt-capable monitor has hub functionality, I doubt you need it.
If you don't already have a Thunderbolt cable for the monitor you're now using an HDMI cable with, be mindful Thunderbolt cables can be expensive. Also, HDMI is not nearly so versatile as connection as Thunderbolt. If stop using your HDMI port, it'll likely be wasted. If you continue not using your Thunderbolt port on your Mini, you might find another use for it (e.g.: external SSD drive).
I'm nowhere near the level some of the Mac gurus on the forum are, so take that with a grain of salt. Unless someone else provides additional info., I don't see that switching to Thunderbolt offers you much benefit.