To my understanding, as the data size did not exceed 2TB, the files should all be stored on the first disk, so theoretically I shouldn't have lost any data.
This may not necessarily be true. The filesystem is merely a set of data structures that describe a single, logical pool of blocks that in your case spanned two physical devices. Although most filesystems tend to fill up those blocks in order from lowest to highest, they can in theory allocate any free block for data storage. Different filesystems use different metrics in their decision-making process of which blocks to allocate, but depending on the age of the filesystem and the options used to format it, the data could be fragmented across both disks with some pieces winding up on the other drive that has failed. This applies regardless of whether you're using hardware or software RAID.
If the drive was mostly used for data storage with lots of files that did not change very frequently, then there is a good chance that they could all be intact on the first drive. But if the JBOD was used as scatch space or an OS boot drive with lots of small random writes happening a lot of the time, there is a higher likelihood that some of that data you wish to recover is now lost.
I tried mounting the first HDD alone but no option combination of
mount had worked.
That is to be expected. The filesystem headers (if
mount can even locate them) describe a layout that is radically different than what a single disk would show. Also, half of the filesystem descriptors, inodes, or whatever (depending on the filesystem) are on that failed disk, so those two things add up to a whole lot of bad/missing/corrupt filesystem metadata that
mount can't handle.
Your only hope here is to use data recovery software. This will be difficult because most data recovery software tries to focus on repairing the filesystem itself, but as discussed, yours is likely destroyed beyond repair.
What you need is a tool like PhotoRec for example. Such tools have built-in understanding of the various file formats they're trying to recover and can scan raw sectors, completely ignoring the filesystem data structures. If the data you're trying to recover is a bunch of pictures or media files, then PhotoRec is the tool for you. Otherwise, you'll need to find one tailored to the type of data you want to get back.