I found where my custom measurement scales are stored. Assuming the folder path to those settings has not changed since Photoshop 2021, this could be an answer.
You haven’t mentioned whether you are using macOS or Windows, so first refer to the Adobe help article
Preference file functions, names, locations | Photoshop
to find out where the settings files are located on your system.
For example, I'm on a Mac, so that document tells me to look in
Users/[user name]/Library/Preferences/Adobe Photoshop [version] Settings
I look in that folder, and I see a file named
Measurement Scales.psp
I am guessing that is the file you want.
It's a text file, so you can open it in a text editor to see what's in it.
So, you can try this:
1. Read that help article to understand where Photoshop settings are on your system, and open that folder on your computer.
2. Look for a folder named “Adobe Photoshop 2021 Settings”.
3. Inside that folder, see if there is a file called “Measurement Scales.psp”
4. If there is, now look for a folder named “Adobe Photoshop 2025 Settings”.
5. Copy the file “Measurement Scales.psp” from its 2021 folder to the “Adobe Photoshop 2025 Settings” folder. It might ask you to replace the current one, and it should be OK to do that.
I am not sure if that will work, but it probably should. I doubt Adobe has changed anything about measurement scales since 2021.
If there is no “Adobe Photoshop 2021 Settings” folder on your current computer, then hopefully you still have a backup of your computer from when it had Photoshop 2021 on it, and you can look in that backup and copy the file from there.
Also, it is possible that the measurement scales could have been migrated (I don't really know), if the settings migration option was on. Because when you install a new version, the installer asks whether you want to preserve the previous version's settings. A lot of people are in a hurry and click through without reading that, and their settings aren't migrated. If your Creative Cloud desktop app is set to auto-update, then the settings migration option is in that app's preferences.