Which of these links actually pass signal?

Plenty of directories advertise backlinks and then ship them with rel="nofollow". You can’t tell from the page. Paste a URL and see every outbound link with its real rel — including the one pointing at you.

What the rel values mean

(none): Passes ranking signal. This is what people mean by dofollow — there is no rel="dofollow" attribute; the absence of a suppressing value is the signal.
nofollow: Tells search engines not to pass signal. Originally for untrusted links.
sponsored: Paid or compensated placement. The correct marking for an ad, and it passes nothing.
ugc: User-generated — comments, forum posts. Passes nothing.

For what it’s worth, you can point this at our own listings — the “Visit” link on a live listing carries no suppressing rel, and a paid sidebar placement carries sponsored, which is what it should be. Checking is the point of the tool.