I just now tried the System Settings>Lock Screen>Show password hints along with Show Message When Locked (be sure to choose this specific option to display the text of your choice) and it worked just fine for me. This is on macOS Sequoia 15.7.
If this fails for you...
Maybe make a custom wallpaper with the text you need superimposed/added onto it. You'll have to get creative with adding text to an image that you want to use. You'll also need to avoid areas already taken up by the existing password text box, etc so that your hint won't be obscured by anything that already exists on the Lock Screen. You could Google this if you need help. This would also only work with that specific wallpaper that you created. if you wanted to change the wallpaper image for some reason, you'd have to create another image with the text.