I wouldn't really describe it as a "middling card", as it's arguably still pretty high-end compared to the cards in the vast majority of modern gaming systems. Performance-wise, the 3060 Ti is typically slightly ahead of Nvidia's 2080 SUPER from their previous generation of cards, and only around 10-15% behind the 2080 Ti, which was the fastest consumer graphics card up until a little over a year ago. It's a good fit for 1440p high-refresh screens, though it should also run most existing games reasonably well at native 4K using "high" settings.
And yes, I would say it's absolutely overkill for 1280x1024, especially since most modern games will probably be best rendered at a 16:9 resolution of 1280x720 on that screen, a quarter the resolution of 1440p. It's okay to use such a display for the time being, though the graphics card will be underutilized in virtually all games. I would definitely look into getting a new monitor relatively soon, so that you can benefit from the increased pixel density and smoother frame rates that card is capable of. 1440p might be nice, but even 1080p 144Hz should be a good upgrade, and be capable of displaying the high frame rates that card is capable of at that resolution. Even a standard-refresh screen at a higher resolution than what you have could be an improvement, though high-refresh 144+Hz "gaming" monitors with adaptive sync (freesync/g-sync) often don't cost too much more. If you have a 1080p or 4K television, you might also consider hooking your system up to that, though those generally won't support inputs higher than 60Hz.