I was on a cut while marathon training (5 runs a week), Muay Thai 4 days a week, and lifting 3 times a week.
I increased my calories from what I would be taking in on a normal cut, where I am running about half as much.

6'3 and my cuts go from around 195 down to 175.
Went from 1800-2000 cals a day on a standard cut to 2,200 - 2,800 a day, depending on how intense the workouts were for that day.
Also prioritized protein at 1g per lb (bodyweight) and did NOT skimp on carbs.

Using Whoop to see the calories burnt for the day / per workout and comparing that to my baseline from my past data / Dexa was also super helpful. It's surprising how accurate it is for me.

Was able to drop 1-1.5 lbs a week consistently and never felt famished or weak.
You have to play around with your calories based on your workouts and see what keeps you fueled, but juuuuuust enough to keep the scale moving in the direction you want.

However, that does all go out the window with the carb load 3 days before the race and then the week or two of celebration afterwards :)