AppleScript that will highlight 32 characters?

At a high level this is pretty easy, although I suspect there's a lot more to this:

tell application "System Events"
	repeat 32 times
		key code 124 using {shift down}
	end repeat
end tell

From an activation standpoint, it's probably easiest to add this in a 'Run AppleScript' action in an Automator workflow. This can be saved as a service, which you can then subsequently allocate a command-key via System Preferences -> Keyboard.

The script blindly sends the keystrokes. It has no concept of which application is frontmost and will receive the keys.

As for it working in a web browser, it does work for me if I make sure a) the web browser is frontmost and b) I'm in an editable text file when the script runs. Ordinarily the right arrow key doesn't do anything on most web pages.

You may need to add additional code to the script to make sure the keys are going where you expect/want them to. I don't know your use case to be able to add this blindly, but this totally falls into the 'suspect there's a lot more to this' category :)

I get what you're trying to do - and maintain that my script will do this. What's missing is how to invoke the script.

If you want to assign a keystroke to it, then your simplest solution is to use Automator to create a Service/Quick action script. This workflow has a single 'Run AppleScript' action with my code, above.

You can use this to limit to working in specific apps (or all apps), and once it's saved you can assign a keyboard command to it via System Preferences -> Keyboard -> Shortcuts -> Services, or add it to your Touch Bar (if your system has one) via System Preferences -> Extensions -> Touch Bar

Sounds like you did all the right things - almost.

I tried it here myself and got the same result - until I changed the key combination to include the command key (so ⌘^→).

I don't remember hearing that Quick Action shortcuts have to have a command-key (in addition to any other modifiers), but it does seem to fix the problem.