New to muscle gain, need some advice

If already doing training - you are likely past the form improvement stage for reason of the gain on the bar.

During that time and a tad after you go through adding weight just to fully use the muscle you got.

After that you have to add muscle to keep progressing - and while you have excess fat - you can do that while in a reasonable deficit. You won't add the same amount of muscle possible while bulking obviously, but you really don't need to gain more fat with that muscle anyway, with a bit still to lose. When under 15% can think that route.

If you still have 15-30 lbs to go - 500 cal deficit is reasonable. 250 deficit when going below 15 left.
And you can make some muscle gains that may not be possible to see until you lose more fat - but you should still have progress on the bar.

You aren't in position for bulk/cut cycles to work well - besides the fact it's more than a few weeks.

And don't lift lighter! It's the heavier weight that says you need this muscle you got - you go lighter in a deficit you are telling body you don't need that muscle.

And should already be heavy for you lifting. And progressing.
You got a 3 x weekly full body type program?
That could be 3 x split program for 6 days a week too.
If trainer is doing a major muscle group 1 x weekly - fire them for jumping on a bro lifting program that is sub-optimal for beginners.

To maintain muscle mass in a deficit - need 3 things - reasonable deficit, enough protein, resistance training.
If enough fat to spare, could even gain some muscle in that deficit.

And there is no such thing as lean muscle except what you order from the butcher. You have no control if it's lean or has fat in it (except endurance cardio) - body decides that - genetics.

Try that, if you want progress on the bar more and willing to accept less fat off the body to see the muscle - nothing says you can't eat at maintenance for a week, diet for a week. Increase weights during the maintenance week, maintain weights during the deficit week. That's more about having more energy and better recovery to allow better benefit from a hard workout.

If you are eating to a goal that MFP estimated, it includes no exercise expected.
You get a deficit from estimated daily burn that is just daily life - if you guessed that correctly.

So all those workouts and not logging it the way the tool works - you are creating a bigger deficit.

No wonder your progress has stopped - one of the 3 things to retain muscle mass in a diet is reasonable deficit.
You are likely not doing that.
You can lose muscle mass even with lifting if diet is too extreme for body. Somewhere.

As you have lost weight off your body, any lifts you are doing using full body weight like squats and deadlifts should have gone up by at minimum the weight lost off your body, and a whole lot more for form improvement and actually getting stronger.
If they have not....

For instance, if you lost 25 lbs since Jan, and your squat and deadlift have only gone up 25 lbs and it feels just as difficult - you've probably lost muscle mass.
Don't count the initial weeks of figuring out what weight to lift, but when it actually got hard and feels just as hard now.
Weight increase should have been a whole lot more than 25 lbs.

Lifting is logged in the database as Weights - it's not much compared to cardio, but it counts though small.
The stairmaster - it probably tells you a calorie burn and watts since it has a motor - use that if you told it your weight, which usually you do have to.
Log it.

Eat to your new goal. That keeps your deficit reasonable.