If you need examples for left wing censorship in the US: the federal government (primarily through CISA) worked for years through NGOs to pressure companies on moderation policy, going so far as to suggest particular accounts or individuals needed scrutiny. California is currently suing several website operators for offering blueprints for 3D printed guns. A few blue states are experimenting with hate speech bills again (typically focused on islamophobia or antisemitism), although they will likely face a successful 1A challenge if they pass.
Both Ds and Rs have been attacking Section 230; Mark Kelly wants to strip those protections when sites “amplify content that caused harm.” KOSA is a looming bipartisan threat.
Left radicals are as virulently against free speech as those on the right, often calling for allies to “shut down” or even physically harm opponents.
Schools are a particularly difficult battleground for free speech, with actions against scholars from both left and right: https://www.thefire.org/research-learn/scholars-under-fire
If you are left wing, you probably don’t think some of these are censorship, others do, that’s why I said it was a good thing that left and right disagree with each other here. In many ways they cancel each other out, although they do a lot of damage to free speech along the way.
It’s also true that currently in the US the primary threat comes from the right, as a consequence of the right being in power. Internationally it is reversed.