I do see `pause-when-empty-seconds` [1] when looking at the wiki, which seems the closest, although I can't find doc on what "paused" means (this is the closest [2]). Looks like a fairly new feature (2024), but it's neat they've thought about it.
[0]: https://wiki.archlinux.org/title/Minecraft/Java_Edition_serv...
[1]: https://minecraft.wiki/w/Server.properties
[2]: https://www.reddit.com/r/admincraft/comments/1k330eg/what_ha...