There is no such thing as neutral. That site is a good example of it: they're personally highly biased towards "centrist" liberal positions to the point that they conflate it with writing "just the facts". They have no consistent methodology, they're just showing you their own inability to detect bullshit when it's something they agree with.

For example, as it has often done in its history, The New York Times has been carrying water for fascistic settler colonial narratives, including hiring an obvious racist to write implausible articles about alleged sexual assaults by Hamas on October 7. Articles contested by the people interviewed, the families and friends of those who died. They censored their own attempts to admit fault and their workers creating media about the errors. Only in the last week have they fired the author in question, which will surely be used to imply that this is the only thing wrong with their consistently biased coverage that focuses almost exclusively on interviewing state department officials, Zionist NGOs, and Israeli government officials.

Did you find any of that on "media bias fact check"? Did it rank the NYT lower than The Gray Zone on its ability to report factually? For having a Zionist bias? Even this one example I've provided is far more damning than anything you've listed.

You can't outsource media criticism, you have to do it yourself and engage with it.