I wanted to let you know that you are not the only one to notice this craziness on Google's API platform. I have been dealing with the same issue as I have for many years been able to simply access the Snippets of my videos and display the video related data on my website.
I used to get 1,000 queries per day and now, all of a sudden, it appears that the "project" needs to be tied to a payment account.

This is so they can now charge you for the queries that you use. Of course, they're not going to tell you upfront how much a "batch" of queries will cost you; at least not until you link your account (payment method).
This can be found in the following location...

This is as far as I've been able to get because I'm just a poor boy from the sticks and can't afford to be paying for queries for data from a resource that I own.
I hope this helps to answer some of your questions anyway.
Hello again @LinuxGnut, I finally got it working. It turns out that once I set up the Billing account in my Google profile and linked it to my API account, I went about deleting everything backward.
I deleted all credentials from each of my projects.
Then I deleted all of my projects (one at a time). This is risky if you have a lot of projects because it told me I only had 7 project slots left. Fortunately, I only need about three for now.
I finally got it working. It turns out that once I set up the Billing account in my Google profile and linked it to my API account, I went about deleting everything backward.
I deleted all credentials from each of my projects.
Then I deleted all of my projects (one at a time). This is risky if you have a lot of projects because it told me I only had 7 project slots left. Fortunately, I only need about three for now.
Then you might need to delete folders as well.
If you have an organization set up, you might want to stop there. I don't have one so I skipped that part.
So, what I'm left with is a Billing account linked to my Google payment account.
Now, I recreated a project, added the YouTube Data v3 API, created new credentials, added them to my application's configuration, and voila! I retrieved the data I needed for all of my YouTube Videos. I hope this helps you out.