Your engine transfers. Your legs mostly do not.
Cross-training gives you two kinds of benefit, and they are not equal. The first is central, your heart and aerobic system: a bigger stroke volume, more blood plasma, better cardiac output. That stuff is fairly general, so any hard aerobic work (bike, pool, elliptical, rower) can build it and it does carry over to running. The second is peripheral and specific: the exact muscles, tendons, and movement pattern of running, the durability to soak up thousands of foot strikes, the downhill braking. That part barely transfers from a bike seat or a pool.
This is why the research keeps landing in the same place. Cycling can raise your VO2max while leaving your running economy flat or even slightly worse, so the net effect on race performance is often a wash. Pool running holds your fitness brilliantly while you are hurt but is not how you get faster when healthy. And cross-training basically never beats sport-specific running for running. So treat it as a supplement and an insurance policy, not a replacement for time on your feet.
The flip side of the rule is the good news. The activities that ARE specific are gold. Uphill hiking is something you literally do in every mountain ultra, so it transfers almost completely. The elliptical mimics the running motion closely enough to be a real bridge back from injury. Lean toward the specific stuff and you get most of the upside with very little of the wasted fatigue.