I would tread lightly with running if cycling racing performance is important to you.
My typical run is/was five miles at 7:15 min/mile pace. I would always feel it the next day with fatigue on the whole body (far more so on pavement which unfortunately is more typical than not). As an every other day affair with biking, I noticed my race finishes were rather poor a couple of times I happened to run the day before a local 60 minute race. The last straw was when I got suddenly and authoritatively dropped from a local fast group ride on a non-consequential hill 15 miles in. When called to really perform, the legs were screaming like I’ve never felt before and I just had to stop. Cycling performance has greatly improved by taking running out of the rotation.
My four-year running experiment is now over, but I do think it helped me develop an aerobic engine at the expense of a lot of running related injuries (knee pain, plantar fasciitis, rolled ankle, and inability to sit in an office chair/car seat for extended time periods). XC skiing has been far more complementary as an off-season activity. Well, that’s my story.
Running at a slower pace and only off-road? Maybe you’ll have a different experience.