Confusion about Scratch Disk

"Scratch disk" doesn't necessarily mean a separate physical drive. It just means an amount of free disk space that Photoshop uses to write temporary working data. 

With SSDs, the scratch disk works most efficiently if it's on the system drive. That used to be different in the old days with spinning HDs, because they had a read/write head that could only be in one place at a time. So writing to a different address meant physically moving that read/write head, which took time. That is no longer a consideration with SSDs, they can switch process on the fly.

As long as you have enough free disk space, wherever it is, you won't get any messages. How much is enough, depends on file sizes, how many files you have open, and how many history states are activated. In fact, history states is the biggest part of the scratch files. Normally I recommend at least 250 GB free space, but for heavy duty work you may need more, maybe up to 1 TB.

If you have the scratch disk on the system drive (default setting), it's in the system temp directory:

scratch-disk-2.png

If it's on a separate drive, it's at the root of the drive.

NOTE - smart objects, and many of the newer AI-based functions that draw on the GPU, do not use the scratch disk. These functions use the system pagefile to keep temporary working data..

Technically Photoshop is always using a scratch disk, it’s only a question of which ones(s). So really you’re asking about whether you should use an external scratch disk. 

…“C” = 1 TB SSD NVMe, 796 GB free of 930 GB … 32GB RAM

By @Klaus5F8D

With 796GB free on your C drive, that is a very large amount of free space for a scratch disk, many users have much less. That makes your C drive an excellent scratch disk and no external scratch disk is necessary, especially if you aren’t seeing problems that could be related to a scratch disk. (I connect an external SSD and assign it as a Photoshop scratch disk because the SSD inside my laptop can fall below 100-200GB of free space.) 

Also, as an NVMe SSD mounted internally, your C drive is by far the fastest storage on your computer. No external can match it for speed (except maybe Thunderbolt 5), and speed is critical for a scratch disk. An ideal scratch disk is as close to the speed for RAM as possible, because it’s kind of a substitute for RAM.

When you put those things together — your C drive is both extremely fast and with a large amount of free space — you have no current need for an external scratch disk.

For your system, I would not recommend assigning any HDD (hard disk drive) as a scratch disk. It would not help, mostly because of its very slow speed. If your computer is current, the NVMe SSD that is your C drive may be able to transfer data at over 7000MB/sec. But most “fast” hard drives can transfer data at only 150-250MB/sec…30 to 50 times slower than a typical NVMe SSD. 

With PS and a large file open, I can NOT find any temp files from PS, not on C or F …?

By @Klaus5F8D

The temporary scratch file is hidden in a deep invisible directory that is not easily accessible, and cannot be changed by a user with normal access privileges. Although I don’t have the exact path at hand, I’d have to look it up. 

If it's working OK now, I'd just use the extra HDD for backups.