How does this happen in practice? Wouldn’t the privately funded news companies still cover the story? Or are all the news companies publicly funded?

In Canada all news gets some amount of government grants and funding. Plus there are various tax programs and breaks related to news to help support them.

People complain that it makes them biased but I don't really think so. At least not currently. For example CBC Power & Politics is decent programming and its not some one sided political overage at all.

In the recent past a lot of Canadian news outlets were incredibly cringe. Woke is now a poisoned word, but they were the cringey kind of woke where any criticism of foreigners for any reason was considered racist. A lot of that was Justin Trudeau Era institutional behaviour that has stared to go away though. The remaining holdovers being some courts and judges mainly.

I think lot of the distrust of news in Canada is a (somewhat reasonable) holdover for when they acted like this.

For Americans reading this though, this is all a completely different baseline compared to American News media. Canadian News might as well be true neutral in to the polarization down south.

Can’t criticize the Liberals because they hold the purse strings. Can’t support the Conservatives because defunding them is explicitly on their platform.

Quite the pickle.

'Free' and 'government funded' are not the same thing. The OP doesn't seem to be government funded.

Also, the BBC has no problem criticizing the UK government.

There's an element of that, but it also exists alongside Postmedia and plethora of other online news media sources. It doesn't serve to replace everything, and as in all cases, getting news from more than one source is necessary to counteract bias and distortion.

All of which to say there are some things that CBC reports on pretty well. I does scrutinize the govt at times, albeit selectively (like everyone else). Maybe the problem people have with it is that it's a public service that has a clear liberal bias.