Very short travel minimalist suspension fork for rails-to-trails riding
It sounds like you don't really need a suspension fork. The surfaces and conditions you describe are what gravel bikes are designed for - those don't have suspension forks, they just rely on larger tire volume and lower pressure (compared to road bikes).
Short travel suspension forks do exist, but if your frame is designed for a longer travel fork the required axle-crown length will very likely be longer than that available on a short travel fork. (Obviously the for longer travel the frame head tube needs to be higher to give the wheel somewhere to go when the fork compresses.)
Short travel forks will also be lower end and therefore lack adjustment and will be heavy.
I'd go with a rigid fork if you can find one the correct length. Of course another option is selling the MTB and buying a (used possibly) gravel bike.