As someone who gains weight to improve my lifts in the gym and then sheds the weight during the cutting process

Basically, your starting body fat percentage predicts the great majority of what you will lose/gain when you diet/overfeed.
So, when you diet, the fatter you are, the less LBM (and more fat) you will lose. Conversely, the leaner you are, the more LBM and less fat you will tend to lose when you diet.
In general, the same holds but in reverse: leaner individuals will tend to gain more LBM and less fat and fatter individuals will tend to gain more fat and less LBM.
When overfed, thin/lean individual will gain 60-70% lean body mass (LBM) while fat(>%15 BF) individuals may gain only 30-40% LBM.

As well, it seems empirically that once body fat gets to the 15% range or so for men, fat gains tend to accelerate during mass gaining phases. I suspect this is due to the development of systemic insulin resistance which causes calories to go into fat stores more readily. Keeping body fat levels below that may be helpful.

I should mention that there was always an anecdotal idea that mass gains were best with body fat about 10-12% body fat (for men, add 9-12% for women). While I had always dismissed this as being an excuse to stay fat, I suspect it’s probably close to correct. Based on what’s going on hormonally and physiologically at both low and higher body fat percentages, this may very well be a sweet spot for mass gaining. You’re fed and healthy enough to lift well and make gains but not so fat that other problems arise.

If you’re above 15% body fat (about 24-27% for women), diet first. If you can get to the 10-12% (19-24%) body fat range or so, I think you’ll be in an overall better position to gain mass.

After finishing your diet, regardless of how lean you get, take 2 weeks to eat at roughly maintenance calorie levels before starting your mass gaining phase. The reason has to do with the physiological adaptations to dieting.

Only try to add mass/bulk until you hit the top end body fat percentage around %13.

Bro the bulk/cut cycle is best just for competing bodybuilders to hit a certain aesthetic on competition day and it fucks with your hormones according to HodgeTwins.

Body recomposition (slow and steady muscle gain and fat loss at the same time) is where it's at.

But anyway, how exactly can you gain muscle while losing fat at the same time unless you're a beginner in the gym?

Ah I must have forgot to consult Youtube to determine my life choices.

You can. It's just highly non-optimized. And it's pretty brutal(especially compared to other ways). My friend Andre did that after he just totally let himself go for almost a year(he's around 145LBM at 5'8" so he's fairly trained). He put on like 25 lbs of fat. Started a modest cut(about 500 under maintenance), and was really hitting it hard 4x a week. He dropped all the fat, and at the end, he put on about 3 lbs of muscle and had an LBM of 148. It also took 6-7 months to gain those 3 lbs.

It can be done even among fairly trained people, but it's a LOT of work, for pretty modest gains. If he'd been lean and clean bulking, he'd have probably put on double that.