Mac: what permissions are granted for "allow the apps below to control your computer"?

Question

I want to use an app from the mac app store (window tidy) but it wants me to give it control "over the computer". This setting is found under security & privacy > accessibility

This seems like a very big umbrella permission, and I can't seem to find out what this actually means in terms of what permissions it grants to apps.

What is the worst that can happen? Can it read my files? Can it make network calls to transfer my files, encrypted files, etc? Can it access contacts, and send emails as me?

I've looked online and this seems quite hard to answer. Does anyone know?

Thanks...

Update based on @teppic's comment below:

$ codesign -d --entitlements :- /Applications/Window\ Tidy.app 
Executable=/Applications/Window Tidy.app/Contents/MacOS/Window Tidy
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
<dict>
    <key>com.apple.application-identifier</key>
    <string>34U5SFK3WS.com.lightpillar.Window-Tidy</string>
    <key>com.apple.developer.team-identifier</key>
    <string>34U5SFK3WS</string>
</dict>
</plist

Update 2

Continuing my curiosity, I installed the network monitoring tool Little Snitch to block and monitor outgoing communications. And in less than 1.5 hrs, Window Tidy (which is a simple app meant to resize windows) has reached out to connect over the network 3564 times. Definitely seems dangerous to have this app have access to read my files and control other apps...

Answer 1

Apps with access to the accessibility API are allowed to manipulate the UIs of other applications (presumably window tidy is using this to resize windows). This gives them the ability to inject events into other processes, and allows them do pretty much anything you can. They can also log all your keystrokes.

Any unsandboxed app (most of them) can read all your files and make network calls.