Help defeating crabgrass while promoting clover

Hello! I am 2nd year new homeowner. I am interested in my yard being biodiverse with low ground cover. Not seeking to eliminate mowing, but still like low ground cover especially good for pollinators. I have been working to add lots of clover in the yard by mixing seed in with grass and filling bare patches with clover. It's been going well, until recently. Recently, I have noticed an emergences of crabgrass. I didn't catch it early on (still learning) and now it's taken over. I am hand-pulling all I can, but it is a lot and I can't get it all. I am noticing the crab grass is outcompeting the clover- especially newly established clover. It's also creating a burden of how to dispose all the crabgrass (its alot). I understand being its mid summer, my lawn might be defeated for the season. I would like to combat the crabgrass and ensure i have a healthy lawn next season. I have looked at herbicides but seem they all kill both clover and crabgrass.

Notes about my lawn: I don't water-but willing to water while growing seed. I don't fertilize. Its grass with lots of clover. Now crabgrass. I have dogs. It gets lots of sun. Located in NJ

Side note: I began composting so next spring I hope to spread compost throughout the lawn to improve lawn health. I don't have much $ to spend on my lawn.

My idea is to keep hand-pulling crabgrass as much as possible. It will die in winter. Will plant more clover early spring and be better at proactively pulling crabgrass in the spring.

Any tips or advice? How do you clover lawn lovers keep away the crabgrass?

TYIA