What’s the name of this manga?

It’s a BL isekai manga; the top is blond and a mage, and the bottom has black hair and helps the top maintain his power through sex. With the cooking skills he has from his world, the bottom is able to teach others how to make new meals. Also, to state, the bottom initially spawned into the world in the middle of the woods and was captured as a sex slave. Eventually, his sister get isekaid to that same worl, and she captured and kept as a sex slave to a pretty bad guy. The mage helps the bottom free his sister, but after, he ends up getting locked up in a cell that’s meant to drain his power. The bottom with help from the mage’s friend and his “power source” (I can’t remember what they’re supposed to be called) break his out of jail, and the mage looks very busted up, which is to be expected—his powers were being drained. In that world, the mages are immortal, so haven’t them in total isolation without their powers is seemingly the worst punishment for a mage. Another thing that COULD help: the mage’s friend’s “power source” looks like bottom, and that’s how the bottom jailbreaks his mage: he puts on a wig and pretends to be the mage’s friend’s “power source”. The mage and the bottom DO fall in love, which makes the bottom apprehensive to go back home. Initially he wanted to go back home because he was the only caretaker for his sister, but now that she’s here, and he’s fallen in love, he wishes to stay.

Help?