If I move established substrate, water, and filters into a new tank do I need to worry about cycling that tank?
Exactly. So, the only thing you bring with old water is nitrate, which is bad, and who knows what else has accumulated. We do regular massive water changes for a reason, so not good to save old water (not to mention it sounds like it would be a pain).Beneficial bacteria are sessile, meaning they live on surfaces, not free in the water. Saving old water does nothing.