Make data on file server (RAID1) still accessible on hardware failure

Solution 1:

When the server hardware (or raid controller) crashes, afaik there is no possibility to directly access the data stored on the raid disks by simply attaching them to a foreign system (sata, usb) without the system having the same hardware raid controller? Is this correct?

Yes, but if you are even borderline professional that does not matter because you have both, spare parts AND a backup that can both be used to get reasonably fast access to the data.

To make the data still available on hardware crash, my intention is the following: Adding an iSCSI target (Synology DS720+) to the network, mount this target on the file server and create a (software) RAID1 containing the hardware raid + the mounted iSCSI target. Now in desaster case, i could simply mount the iSCSI target on any other machine and access its data.

And that would be better compared to a spare raid controller (WAY cheaper) and a backup (WAY safer) how? Note that while it may handle a hardware failure reasonably fast (at the cost of performance) you are still totally open to data manipulation (i.e. through a failing memory chip) - which a backup ALSO allows you to roll back.