It's not entirely true that US (or EU) did nothing. In the interview you're quoting from, Navalny e.g. gives the example of "oligarch" Roldugin (as both friend of Putin and corrupt). But his businesses were investigated (at least in the EU) prior to Navalny's 2016 interview, e.g.
All the transactions were executed through Ukio Bankas in Lithuania, where about half the Troika Laundromat companies are known to have held accounts. Lithuanian regulators shut Ukio in 2013, alleging poor asset quality and compliance. The bank’s principal shareholder, Vladimir Romanov, absconded to Russia. In 2014, the Russian government officially refused to extradite the banker to Lithuania.
Furthermore, I think you (and possibly Navalny as well) are exaggerating the scope of US laws. Criminal investigations for corruption abroad e.g. under FCPA need involve at least a foreign company with a US subsidiary. The US administration is entitled by other laws (Magnitsky Act, IIRC) to sanction foreign individuals it deems corrupt (by freezing their assets in the US), but that [alone] doesn't give basis for initiating a criminal investigation (in the US) against those same individuals.
N.B. looking more closely at what's sanctionable under the Magnitsky laws, it's only connection with human rights abuses, so not even corruption per se. It is more tenuous to sanction business people for being connected to Putin's government and thus (indirectly) to human rights abuses thereof, which probably explains why there wasn't a US "‘KleptoCapture’ task force" targeting Russian oligarchs before the war.
On the other hand, there is however a (newer) 2020 US act that does seem to allow sanctions for corruption alone "Section 7031(c) of the Department of State, Foreign Operations, and Related Programs Appropriations Act, 2020", and this was already used last year (well against Ukrainian "oligarch" Kolomoyskyi), but this law is limited by its wording to barring entry into the US thus allowing less of a punishment than even freezing assets, let alone criminal prosecution.
As far as I recall US immigration law already allows barring entry for "moral turpitude", so probably the only real goal of the 2020 law is to enable public announcements shaming the targets even if they don't actually intended to enter the US.
By the way, somewhat contradicting a comment under the Q, it looks like the US did charge one Russian "oligarch" Konstantin Malofeyev for evading sanctions.
The DOJ claims that Malofeyev
conspired with Hanick and others to illegally transfer a $10 million investment that MALOFEYEV had made in a United States bank to a business associate in Greece, in violation of the sanctions blocking MALOFEYEV’s assets from being transferred.
But the indictment also notes Malofeyev is in Russia, so not arrested. The facts imputed date back to 2014-2015. Also, this was a sealed indictment. We know it was unsealed in April 2022, but we don't know exactly when it was filed (sealed). But "December 2018" also appears mentioned in the indictment (as the end date of a conspiracy charge), so the indictment had to be issued at some point after that. (N.B. Hanick was arrested [in London] "in early February of this year — just weeks before Putin launched his balky blitz of Ukraine".)