If an app says "I'd like local network access to find other copies of myself", and you say yes - you're not giving it permission to find other copies of itself. You're giving it all local network access.
If you give it 'full disk access' because it wanted to access one file, and 'local network access' because it wanted to scan for copies of itself - you've given it full permission to export all of your data to your LGTV.