From my personal experience, I am slow charging my iPhone 13 by powering it off after connecting it to the charger. If it was on, then it would be fast charging. This slow charging causes no increase in temperature of my iPhone at all. I live in an area where ambient temperature is already quite high. Coupled with the heat generated from fast charging, the iPhone gets noticeably hot to touch. I have a MacBook Air M1 and I use the 30W adapter of the MacBook with the lightning cable that came with my iPhone.
Regarding optimised battery charging, I have found conflicting opinions on whether it works when phone is powered off or not. I have been informed it works even when phone is powered off by some people sharing their experiences, whereas others tend to agree on what you mentioned. I personally don't have a set charging routine, so I haven't noticed optimised battery charging take effect even when phone is powered on.