I have dedicated and virtual servers at OVH and Hetzner and other companies. I'm quite confident they don't scan for anything on the hard drives. One of the selling points of Scaleway.com's C14 backup product (previous incarnation, don't know about current one) was that the storage was encrypted and that they would delete their copy of the decryption key if you checked a box. If you chose that option, you could not restore your backup without re-entering the key (block of hex digits that you had to copy on making the backup). It wouldn't surprise me if that resulted in the obvious sob stories about lost keys.

Those are not US companies but I've never heard of AWS, DO, etc. scanning people's storage either.