Alright update... Some settings have changed since it was simple apps. Both apps just do automatic backups now instead of just working from a file. It still works to do backup, but not import. I remember I used to be able to do it with all simple apps, where it does nothing but read write a file. So you have to treat your phone copy as your canonical source. Don't use simple apps though, they were bought by a spyware company, hence the fossify fork.
I think it has to do with android preventing apps from getting access to the entire internal storage an android version or two ago, where now apps only have access to read/write to one directory. There are apps that let you sync from a local file to system contacts and calendars to bridge the gap. ICSx⁵ is one that does this for calendars. For contacts, OpenContacts does what I said Fossify contacts is supposed to do, but it is designed around keeping a separate contacts aside from your system contacts so that other apps can't see your contacts. I only know that because I had to use WhatsApp for like a week and so I needed to prevent it from getting my contacts. I might switch back to it now actually.
Sorry for the outdated information, I hope this all was helpful.