Automator workflow asks for Accessibility permissions in every app

I've made a service from a very simple automation with AppleScript.

The service is triggered by the keyboard shortcut ⌘ + period and will open the "About" window for the active app.

on run {}
	tell application "System Events"
		set frontmostProcess to first process where it is frontmost
		click menu item 1 of menu 1 of menu bar item 2 of menu bar 1 of frontmostProcess
	end tell
end run

The problem is that every app that I trigger this shortcut in asks for the Accessibility permission. Once the permission has been granted for an app, the service works without permission prompts for that app.

The idea was to introduce a shortcut similar to ⌘ + comma which is a macOS default shortcut that opens Settings in any app.

Is there a way around this permission issue? I've tried running a shell script that runs the same AppleScript, but it did not make any difference.

The service:

The automation:

System prompts 1 and 2 that show up after the shortcut is triggered: