That’s not how Do Not Disturb works. First, almost all IP phones have a Do Not Disturb softkey enabled on them “out of the box”. That DND key will put the entire phone in DND mode regardless of how many SIP accounts are on it. When a incoming call hits the phone DND causes a 486/480 SIP Reply showing the phone BUSY.
The FreePBX Do Not Disturb via Feature Codes/UCP changes the State of the extension to BUSY so the system doesn’t dial the extension and treats the extension as BUSY because that’s how it would end up being treated if the phone was in DND mode directly.
DND doesn’t care if the phone makes outbound calls, DND stops the phone from receiving inbound calls. It is meant to tell others “I’m not taking calls now”
As for what the actual device shows for the various status or modes, that’s up to the maker of the device. There are no settings that will make a LED/button on a phone blink or not blink in a specific setting.