Can I do mesh tape over the cracks as they are (with some initial sanding to remove high points), or do I need to strip it down to drywall first? Getting down to drywall would be tricky without damaging the drywall

Any settling should be long finished. The bedroom is on the second floor, and the additions that border these walls were completed ~30 years ago. The drywall in this room predates that addition, but these cracks are through layers of paint that came after the additions. Upon further inspection, I think the weak drywall is limited to a much smaller area than I first anticipated. That area has no cracks and will be trimmed with a cover out in for better plumbing access anyway.