I love this topic! I ran through all three of my pregnancies and feel very fortunate that I was able to. My midwife was the one who gave me the best advice 'It's your body and you know it best, but there is no such thing as no-pain-no-gain in pregnancy so know when to stop if you need to'.
I used the belly belt, particularly in the 2nd trimester when the round ligament pain was the worst and then did a lot of hike/running towards the end. I will say it helped with anxiety and with sleep. I had a particularly irritable uterus (yes, they actually call it that) and so it also helped to calm those contractions.
One other thing to watch for is the relaxin hormone that is necessary for birth and in your body throughout your pregnancy, it caused some loose joints for me which resulted in a sprained ankle in my first pregnancy and plantar fasciitis in my 2nd. I ran the day before I gave birth with my third so maybe I learned my lesson by then.
Regardless - I think it's important to do what feels good for you. Pregnancy is a natural and really beautiful, miraculous thing, it's not an injury and shouldn't keep you from moving your body and staying active.
