I gained tons of 0dr blogspot backlinks...

Strangely these all count as 1 referring domain each. But since their DR is 0 and they are not tier built, I doubt they will have any impact on my ranking.
However, what I am concerned is that I might get penalized for it.
I honestly don't know about these... are they going to be impacting my site? I don't even know why someone is blasting my website.

That's a common spam that has been going on for years. Basically every domain has it to some extent. Some more, some less.

Ahrefs actually catches these, Majestic just ignores them and not sure how Semrush treats them.

All in all, absolutely nothing to be worried about. It's just annoying.

They're part of the flotsam and jetsam of links that your sites will pick up if they actually rank for anything. Messes up the look of your backlink profile for sure, but I doubt it's a personal attack.