I had the opposite experience going from a OnePlus 8T stock to Lineage OS. Having root means being able to reduce the amount of apps and wake up — no google play service was the key. This was a while ago but I went from 1-2 days of battery life to about 4-5 days. This is with light use, screen on time was equally draining with both setups.

I would assume that an iPhone has similar amounts of unwanted background apps and would also be able to gain battery life instead of losing it if rooted. Obviously if you install spyware, you lose a lot of battery life. Funnily enough, I remember that a few years ago, people were surprised to find that uninstalling facebook increased battery life because it behaved much like spyware.