This is a good question and I appreciate you asking it, shows you have a good heart. As long as you just communicate in some form, that is automatically less douchy than most guys who will just ghost.

The most gentle way to say it would be “hey, I’m sorry we haven’t hung out lately. Things have gotten hectic in my life and I don’t feel like I can give you the attention you deserve right now. Instead of stringing you along waiting for my schedule to open up, I just wanted to let you know I’ll be off the grid for a few months taking care of shit. I really valued our time together though ❤️“

It depends on the context whether you were actually banging this girl or talking over text. Generally, the right way to go is a white lie "Hey. You seem really cool. I wound up working things out with my ex and don't think it would be fair to either one of you if we keep hanging out. We should be friends though"

I basically make it clear (often very early on), that I'm not going to be with one person. A line I'll use is "More than anything, I value my time and freedom. I want to not owe those to anyone besides myself". Then, when/if a girl is demanding of my attention, I'll reference that and say that I think it's best that we stop hanging out for a while.