Harddisc partitions, it's a mess

While the display is bit confusing, what you are seeing is completely normal.

Just some clarifications. With the APFS file system Apple now uses, a container is what was traditionally called a physical partition. Now Volumes are subdivisions of that container. While they are somewhat related to what was once called a partition, they are not fixed in size and can grow as needed within the container. Basically they are more analogous to a special directory that only APFS can manage at a very basic disk level.

Broken down somewhat clearer in Terminal, the actual physical drive looks like this:

/dev/disk0 (internal, physical):

   #:                       TYPE NAME                    SIZE       IDENTIFIER

   0:      GUID_partition_scheme                        *500.3 GB   disk0

   1:             Apple_APFS_ISC Container disk1         524.3 MB   disk0s1

   2:             Apple_APFS Container disk3         494.4 GB   disk0s2

   3:        Apple_APFS_Recovery Container disk2         5.4 GB     disk0s3

#1 and #3 are special containers (partitions in old speak) used for booting and recovery.

/dev/disk3 (synthesized):

   #:                       TYPE NAME                    SIZE       IDENTIFIER

   0:      APFS Container Scheme -                      +494.4 GB   disk3

                                 Physical Store disk0s2

   1:                APFS Volume Macintosh HD            10.3 GB    disk3s1

   2:                APFS Volume Preboot                 7.6 GB     disk3s2

   3:                APFS Volume Recovery                937.2 MB   disk3s3

   4:                APFS Volume Data                    122.4 GB   disk3s5

   5:    APFS Volume VM                      1.1 GB     disk3s6

This is the volume structure of "Apple_APFS Container disk3". All needed by the Mac. #4, APFS Volume Data, contains all the apps, data, user directories, and a working version of macOS. All the others are needed by macOS or by APFS and have no connection to the user.

So, bottom line, all those items are needed and absolutely necessary and should not ever be messed with other than the instance of reformatting the entire drive in preparations to install macOS.

It appears you have two "Data" (or "Daten") volumes. It is really hard to make sense of your setup because of the blanked out names, but I believe only the first "Data" volume shown is associated with your current OS installation (associated with the current boot volume). The second "Data" volume is no longer associated with the macOS boot volume (if it ever was).

If you don't have any important files in the second "Data" volume (the one you have listed as "HDisk"), then you can delete it if you wish. Disk Utility won't allow you to delete any volumes which are associated with your current macOS installation (you must be booted to the internal OS to have this protection). Just make sure you don't need any files located in that APFS volume prior to deleting it.

"Harddisc partitions, it's a mess: [...]I guess this happened during the swap of the Mac, installation of Time Machine devices etc. ... what should I do, make a new backup and reformat the whole thing?"

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Thank you for the screenshot.

Ridding Of Unknown Partitions:

So, it this macOS currently installed? If so, create a Time Machine backup, and then transfer it all over. Format the disc with the corresponding format, and then install the macOS. Once installed, perform the data transfers...

A. Transfer Items Manually.

You'd export items to an external drive, and then import it to the new Mac.

And/Or...

B. Import, then Delete:

Other than manually transferring they, you do so the traditional way (which you seem to want to avoid): Use Migration Assistant to back up your Mac with a Time Machine Backup, and then import items as a whole. Once imported, delete as desired.

+1 That is normal and there is nothing for you to see or do there.

You should ignore, the same as Disk Utility does when it first opens.