Ironically the Media Bias / Fact Check site you have linked also has a long track record of being arbitrary and reflecting the author’s opinions, basically. See what CJR wrote about them in the section titled “armchair academics” here:
https://www.cjr.org/innovations/measure-media-bias-partisan....> [Media Bias / Fact Check’s] efforts suffer from the very problem they’re trying to address: Their subjective assessments leave room for human biases, or even simple inconsistencies, to creep in. Compared to Gentzkow and Shapiro, the five to 20 stories typically judged on these sites represent but a drop of mainstream news outlets’ production.
I’m not a frequent reader of the Daily Wire but have read articles from time to time and haven’t found factuality issues any more so than other news sites. Glancing at their front page right now, nothing seemed obviously off. They have their own selection bias of stories they cover but that’s because they’re meant to be the answer to a lack of coverage of the same topics or same perspectives from traditional news media.
EDIT: looks like you added more links. I don’t have time to go through them all but The Daily Beast and Popular Info (run by Judd Legum, formerly of Think Progress) have a strong left bias. As for the Snopes fact check you linked, it is authored by Bethania Palma who authored an embarrassingly bad fact check about AOC’s account of the Capitol riot recently (https://www.allsides.com/blog/media-bias-alert-snopes-fact-c...). It seems you’re listing out a mix of anecdotal examples and opinions from people who themselves have political bias reasons to discredit The Daily Wire.