I've seen that siege on/off when moving units now with my other siege.Yes, it stops the city from healing.
Sometimes, just moving one or two units one tile over can start or stop a siege. Have you tried that?
If you are on a device that can see links below this post, there is a link for ZOC that explained those rules and there is also a good one on city combat that includes sieges
Most are in the path Downloads- Civ 6 downloads - general reference guidesApparently I am on a device that cannot into links lol
Most are in the path Downloads- Civ 6 downloads - general reference guides