That episode has near no coverage in English, and I don't think much of coverage in Russian survived to this day.

But here is it in basics:

Russian opposition was completely dominating the Internet at the time, before around 2005, a complete opposite of the picture on the TV, and fake opinion polls.

Kremlin was not happy, and went straight to the Internet's "kingmaker" — Google (or maybe it was the other way around?) Publicly it was to get its officers "taught" about internet media, but the writing on the wall was way more obvious.

At around late 2005, Google announces them "optimising their algorithms against abuse," and within weeks opposition's websites start to disappear from Google one after another. Google obviously claim "we did not hardcode anything," but simply rearranging the word order in search was enough to expose them doing that.

At the same time, we saw a wave of very weird adsense political ads on sites associated with opposition, and a wave of exhilarating pro-Putin drivel in Western media, clearly suggesting they got some Western spin masters on their side now.

There is an easier explanation: Kremlin just started to spend money on its Internet presence and opposition could not match it, which got amplified by more people getting connected to the Internet (thus instead of tech savvy crowd sympathetic to opposition, you get a bigger share of conservative "simple man"). Opposition just got relaxed and thought that Internet will be their home ground forever. And it's far easier for opposition to blame Google for collusion with the government, than to work hard on quality of their websites. Compare the old "non-systematic opposition" influence with the drive behind people like Navalny and you can see that there is no conspiracy, just laziness vs hard work.

Even that wouldn't mean nearly all opposition media vanishing from the Internet in the span of few weeks.

Any independent confirmation of those allegations?

In my personal experience Meduza articles are near the top for some topics and several years ago Dozhd was popular as well, also sometimes I get links to opposition LJ blogs. Also there was a large shift to Telegram channels from traditional websites.

It would be really helpful if you could link to a source for this information, even something of ill repute.

Um, I thought Yandex was the dominant search engine in Russia, not Google?

It wasn't really, it only managed to clearly dominate long after Google's interest in Russia cooled down.

It's a blatant lie. Google never was as dominant in Russia, as in the US or Europe, at best times it had 50-60% of market share (mostly thanks to Android popularity). In 90s Russian market had quite popular Rambler and Apport, whose share got mostly absorbed by Yandex later.

I suggest that you read that account's post history before you believe their claims.

I read their history, and I don’t know what you mean with this comment. Could you link to specific examples? I don’t know them, but their comments seem well reasoned.