To put on muscle: you need to stimulate the muscle by lifting and provide protein, and provide additional energy in the form of carbs and fat to enable the protein to be used for building muscle
To lose fat: you need to stimulate the muscle by lifting and provide protein, so that your body knows it needs to keep the muscle, and then you can manipulate carbs, fat, cardio and meal timing to burn fat
Research reviews say the “optimal” amount of protein is something like .82g per pound bodyweight. Which, if you’re at 18% bodyfat, is 1g protein per pound lean-body-mass.
Anecdotal evidence says anywhere from .8 to 1.5g protein per pound bodyweight. In fact, a lot of it says you need MORE protein when losing weight than you do when adding muscle.
This is based on my own review and reading… but… heavy lifting should be used for both gaining and losing. While at a surplus, you should be getting stronger and/or getting bigger. While at a deficit, you should try to maintain, but many people end up getting a bit weaker. By heavy lifting, I mean something heavier than your 6RM.
Volume seems more relevant when addressing size than it does strength. Either way, most strength-based programs include a decent amount of volume (at least with “accessory” work), and most size-based programs are built very much around volume.
I haven’t found anything – by people who’ve successfully cut weight for a physique or bodybuilding competition – that suggests that more or less volume should be used while cutting. The very last week for a competition, I’ve seen the volume ramped up just to deplete glycogen… but outside of that, nothing.
I admit that everything I’ve read is heavily biased by the writings of the authors on this site, and the successes of the lifters on this site, some current, some in the past.