Unpopular opinion: limiting screen time is worth the battles
My kids complained nonstop for two weeks when we went to max 1 hour a day on weekdays. Now six months in they actually play outside, read more, and stopped the constant whining about being bored. Yeah it was rough but worth it. Their moods are better too. I know everyone's different but if you're on the fence about setting limits I'd encourage you to stick with it past the initial pushback.
The battles are real but you won. Most parents don't have the guts to stick with limits this strict. Respect for seeing it through.