If it's not open-source, but the protocol is documented, see above.
If it's not open-source, and the protocol isn't documented, well... that makes the decision easy, doesn't it?
I've used enough Claude coded applications that I wouldn't trust that with a backup, unless it had extensive tests along with it.
I can audit and verify Claude's output. Code running at BackBlaze, not so much. Take some responsibility for your data. Rest assured, nobody else will.