Selecting an External drive in Photoshop save window takes forever to load

There’s a passage in that Adobe article that I didn't notice before. It seems to help address an ambiguity that was leading some to believe that Photoshop doesn’t support external hard drives, because it helps distinguish the difference between network drives/network attached storage (NAS), and external hard drives/direct attached storage (DAS). It clearly states that Photoshop supports the use of DAS external hard drives (end bold formatting is mine):

Important: External hard drives should work with Photoshop without a problem, although depending on how they are connected, might be slower than working with files on your internal drive. Testing against these drives by temporarily disabling them and working exclusively on an internal drive is appropriate. However, Adobe is not stating that there should be regular problems storing files and working with external hard disks.

So, there should be no problem using directly attached external volumes. If there is a significant delay loading a specific volume, that is worth troubleshooting as we are doing here.

By the way, I am also using macOS 13.6.6 on an M1 Mac with all originals on external SSDs, and I have not generally seen that problem using multiple Adobe apps with those files on external direct attached storage.

However, I did recently have a problem where one of my external NVMe SSDs was taking forever to mount. It was increasingly annoying, because I had other similar drives that mounted right away. One day I decided to open Apple Disk Utility and run First Aid on that slow-mounting SSD, and it reported finding problems with the file system that it said it couldn’t fix. So I copied all of the files to another drive, reformatted the troublesome SSD, and copied all the files back onto it. Problem solved, no more delay. Now, I can’t guarantee this is the same cause of or fix for your problem, but if you haven’t recently run First Aid on the SSD, it would be worth doing.

Also, your SSD is formatted Mac OS Extended (all of mine are now formatted as APFS). Technically that should be OK, and should not be related to such a long access delay, but it’s just another difference I noticed. If you do decide reformatting is in order, consider trying APFS for the performance and efficiency benefits, unless you need that SSD to be read by older Macs that don’t understand APFS.