[NY] How much does a job title really matter for future roles?

I recently got offered a position at my company that comes with more responsibilities and a small pay bump, but the title isn’t exactly what I was hoping for. It’s something vague like “Operations Coordinator” instead of something that actually reflects the work I’ll be doing. I’m torn because the experience itself will be good, but I don’t know how much recruiters or hiring managers care about the title itself when looking at resumes. Will they assume I don’t have the right experience just because of the wording? I’ve been stressing over it more than I probably should. The other night I was just sitting on the couch and caught myself overthinking the whole thing again. So I figured I’d ask here: when it comes to moving up or applying for new jobs, do titles make a big difference, or do people mainly look at the responsibilities and accomplishments listed under them?