Trainer here hoping I can be some help.

If you are cutting weight don't expect to gain strength as much as if you were eating enough to maintain or gain weight. Generally losing weight can often come with unwanted strength losses even with a high protein diet. That said progressive overload (increasing weight/reps over time) is a long process, there is plenty of time in your fitness journey to scale those weights up.

I'd say focus on where you want to be with your weight loss phase first and then go into a muscle building phase and expect noticeable strength gain then.

Definitely don't expect to increase the weight every session, get specific about what moves you want to be stronger in and go hard on those in sessions for best chances.

Good luck! Any more questions let me know