Without paying for remote backups, can I just manage my own backup on my own hard drive, and restore it when I want to?
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I do that and then sync that folder with another computer using SyncThing.
AFAIK SyncThing only monitors for changes between files with matching names, and Signal stores each backup with a separate (timestamped) filename. Are you storing every day's backup individually, or do you have some tool for deduplicating?
That also means that Syncthing can't do better than sending the full backup. But if you're syncing via wifi (e.g. at home) it's not really a problem anyway.
Would you mind elaborating on why this would be an issue? 1) Tools like borgbackup provide the exact functionality you're describing and considered secure. 2) Encrypted file systems also don't re-encrypt your entire HDD whenever you change a single file.