I'll be watching for it.

I'm not sure why it happens, although using a VPN can cause it. Try opening the thread that you've linked to in your OP above in an Incognito window, or Private window, or whatever the private browsing mode is called on your browser. You may find that the video doesn't ask you to sign in.

It's going to happen on any site where you see an embedded YouTube video. It's probably either related to cookies or to your IP address, but since you just tried Incognito mode and that didn't solve it, maybe cookies aren't the problem. If you're not using a VPN, you could try using one, at least temporarily...

Anyway, as mentioned this issue is specific to you -- other people can see the video that you posted just fine.

It's also possible that the problem might clear up by itself after a while.

If you turned off your wifi and connected through a cellphone connection, you changed your IP address. YouTube didn't block you when you did that, which suggests that your wifi's IP address is being recognized by YouTube for some reason, and they want you to sign in to watch videos. When your wifi's IP address changes, which it will eventually, the problem should fix itself. However, the amount of time it takes for this to happen can vary, and it could be quite a while depending on your ISP.

To clear your browser's cache and cookies, use the keyboard shortcut Ctrl+Shift+Delete (or Cmd+Shift+Delete on Mac) in most browsers, select "All time" for the range, check the boxes for "Cached images and files" and "Cookies and other site data," then click "Clear data" or "Clear now" to remove temporary internet files and site preferences. This helps resolve website issues, but you may be signed out of some accounts.

​https://help.heysummit.com/en/articles/10513755-troubleshooting-sign-in-to-confirm-you-re-not-a-bot-error-when-using-youtube
How to resolve it:

While we cannot control YouTube's security settings, there are a few steps attendees can take to resolve the issue:

Clear browser cache: Clearing the browser's cache can sometimes resolve the error by refreshing stored data.

Workaround using the video URL:

Right-click on the area where the video should be playing (where the 'Sign in to confirm you're not a bot' message appears).

Copy the URL of the video.

Open a new tab in your browser, paste the URL, and try watching the video from there. This has worked for most attendees experiencing this issue.

I click "watch in on YouTube instead of in the post.

But you fixed it, so it's all good.