Making the macOS Special Character Popup Menu Appear Everywhere
I don't recall coming across a way to customise this on an application by application basis, but something that may work as a bit of a workaround is using the Character Viewer in the menu bar.

More specifically:


Go to Apple > System Preferences
Select the Keyboard preference pane
Ensure you have the Keyboard tab chosen
Select the third checkbox to show the keyboard and emoji viewers in menu bar
Now your menu bar will have an icon looking like this:





Now, regardless of the application you're in, you can select the Show Emoji and Symbols option from the menu bar
Now the characters you're looking for are listed under the Latin category on the left.
Now you can just double-click on a character to insert it into Adobe Illustrator or Photoshop.


TIP: - Once you start using this, your frequently used items will appear within the Frequently Used category. You can also select particular characters and click on the Add to Favorites button so they're easier to find/use.