I think the get staffId in NumberedBarRendererFactory might be referencing the wrong thing.

[goodgame365]

The correct implementation should be:
public get staffId(): string { return NumberedBarRenderer.StaffId; }

the erro:

public get staffId(): string { return SlashBarRenderer.StaffId; }

[Danielku15]

Yes, that's indeed an oversight. Impact should be fairly small but there is one. (e.g. when having ties/slurs on the numbered notation)

[goodgame365]

Yes, currently it seems there is no impact. However, my user wishes that if there is only one Numbered track, the instrument name and parentheses should not be displayed. Therefore, I need to determine whether to display them based on this condition

[Danielku15]

As I tried to highlight so often: Please share such use-cases 😉. There might not be a need for you to patch out the alphaTab code for such things but we can make such things features (if not yet available).

For the numbered-track only you could simply do something like the following. Call updateDisplay whenever the displayed tracks are changed (e.g. scoreloaded or before you update the tracks via your UI).

function isOnlyNumberedNotation(tracks) {
	let onlyNumbered = true;
	
	for(const t of tracks) {
		for(const s of t.staves) {
			if(s.showSlash || s.showTablature || s.showStandardNotation) {
				onlyNumbered = false;
			}
		}
	}
	
	return onlyNumbered;
}

function updateDisplay(tracks) {
	if(isOnlyNumberedNotation(tracks)) {
		api.settings.notation.elements.set(alphaTab.NotationElement.TrackNames, false);
	} else {
		api.settings.notation.elements.delete(alphaTab.NotationElement.TrackNames);
	}
	
	api.updateSettings();
}

Which "parentheses" do you mean?