When Notion Will Not Embed a Site
Sometimes the embed is fine and the site is the one saying no. Plenty of sites send a header telling browsers they must not be loaded inside another page, and when that happens Notion shows an empty frame or a refused to connect message. There is nothing to fix on your end, because it is a decision the other site made.
Who does this
Banks, most social networks, and nearly anything sitting behind a login. It is a security measure rather than an oversight, so it is unlikely to change.
Telling it apart from a broken link
Open the URL in a normal browser tab. Loads there but blank in Notion means a framing block. Fails in both means a dead link. That one test settles it in about five seconds.
The login case
Sites that need you signed in are related. The embed loads a fresh session with none of your cookies, so you get the login screen instead of your content. Looks broken, working exactly as designed.
What to do instead
A button pointing at the site. Less pretty, always works, and it makes the destination obvious rather than hiding it in a frame.
thePlus.so widgets are built to be framed, so if one of ours is blank it is something else and widget not showing is the page you want.
Stricter hosts than Notion
Notion is fairly relaxed about what it will frame. Google Sites is stricter and refuses more, and some WordPress security plugins block iframes from domains you have not allowed, which produces exactly the same blank frame from the other direction.
If a widget works in Notion and not elsewhere, look at the host's settings before assuming the widget is at fault. That is nearly always where the difference is.