Many thanks to all those of you who replied to my question about Dropbox alternatives recently.
Many of you suggested Nextcloud, and having played around with it for a bit, I think it will do nicely.
So I am now embarking on the surprisingly complex project of moving everything I had in Dropbox to Nextcloud.
Thanks also to whoever it was who suggested Hetzner for hosting Nextcloud, which seems to work nicely.
Reducing my dependence on US tech, one service at a time.
@statsguy I used to have a Synology NAS, which did all this stuff for free. I've now moved over to a roll-your-own solution. All linux-based and hosted behind my sofa, and I can tell you what I use if you want, but suffice it to say that I found Nextcloud to be overly complex and functional for my needs (and hence, prone to going wrong) and there were aspects of the alternatives (ownCloud, Seafile) that I didn't like either.
@dave The "prone to going wrong" thing was one of the main things that persuaded me to use a 3rd party hosting service rather than hosting it myself.
Another one was that this way I get the backups off-site. Hosting it on my own server wouldn't keep my data very safe if my house burned down.