Repairing cracks in plasterboard ceiling - ok to tape over paint?
Use fibafuse tape not mesh or paper.
Option1... the best way but more work:
If the cracks are bad the proper way to do this is to take an oscillating tool preferably with a grout removal blade and cut out the crack all the way down to the lath (this will make a bit of a mesS). Make sure all loose material is removed. Then fill the crack with Durabond 90 making sure the mud mixture is thick not soupy. Push that mud into the old lath board. After it’s dried you might need to apply a second coat. Make sure surrounding  area is clean. Apply fibafuse tape with all purpose mud. Now do finishing coats.
Option 2...
Scrape off any loose paint. Clean surrounding area. Embed fibafusefuse tape NOT MESH TAPE in all purpose mud. Now do finish coats.
Your probably going to get some bubbles In your mud since this is a painted surface. It’s just going to require sanding and skim coating to fix. All purpose mud is important when embedding the tape as it has glue in it.