> The size of Sync is actually fairly small for me, it's just 12GB, but it's not small enough to fit on my 128GB phone.

Synctrain is a great iOS syncthing client that connects to your swarm but doesn't actually sync any files (unless you ask it to). You can still browse the contents of your shared folders and selectively download individual files.

https://apps.apple.com/us/app/synctrain/id6553985316

They seem to be about twice as expensive on a few openweight models I've checked.