Correct upgrade path from 8.2.5 to current

I am running OC 8.2.5 on a QNAP NAS and due to the low performance of this system I want to move the installation to a new machine. And I want to upgrade to the current stable version.

In the official installation instructions I can not find explicit instructions for an correct upgrade path.

I understand that the manual update process supports only one step to the next version. Of course I want to go the most direct but still safe way. So what is the fastest way in my situation?

Judging from this issue, I wouldn't upgrade to OC > 8.2. For security reasons, you should however use the latest version of the 8.2-branch:

this restricted environment is one of the reasons I want to change to another machine, not neccessarily a QNAP-system. I may use a real server hardware running Ubuntu Linux (I'm not keen on doing this because of the responsibility to keep the whole system all the time updated by hand, but I miss to much flexibility on the QNAP firmware that I'm considering this way)

So the update/upgrade path I guess would look like this:
1. Installing the OC 8.2.5 server on the new Ubuntu Linux machine
2. copy all database and file content to that machine
3. When the OC installation was successfully moved (means it runs error free) to the new machine, continue with the update procedures

Is that correct?

Yes, that is how i would do it.