What is a "loop way"? I googled it together with Linux and file and did not find anything.
The proper term is "loopback filesystem".
Is this simply like a separate file that is LUKS-encrypted and I would then mount it for remote access?
Yes, it's a filesystem in a file that you mount with '-o loop'.
If so, what would prevent the hosting company - which I presume is the root user - from also accessing it?
You provide the decryption password when you mount it. Once the filesystem is mounted anyone with the appropriate permissions can read it. You can reduce the opportunity of someone accessing it by only mounting it when you need it and unmounting it as soon as possible.
TBH, if you don't trust the root user of a system, then there's not much you can do - there are just so many ways a privileged user can get access to things, both "legitimately" because of their absolute access or "covertly" using trojans and so on that you would never know about. If you have legitimate concerns about the hosting company, then find a different one.
P.