Why did Russia offer autonomy for Syria’s Kurds?

What do you mean by "Kurds"? I suppose that you mean the YPG/YPJ (or "SDF" - their Pentagon-given name). The YPG/YPJ is being supported by the United States for the most part, but they also collaborate with Russia and Assad to some extent and have done so for quite a while (for example when they shelled a minibus of fleeing civilians that was trying to get out of Aleppo a while back).[1] In that light their support for Rojava isn't really a surprise anymore.

The FSA isn't really "US-backed" as much as many people want you to believe. The only faction of the Syrian revolutionary forces that was backed by the CIA and is controlled by the US-supported MOC is the Southern Front, and they have recently been told to stop attacking Assad.[2]

Since the Syrian Arab revolution is pretty much doomed now I can see a deal between the PYD and the Assad regime happening, but it wouldn't be a very stable one. There will eventually be uprisings again and there is still the conflict between Turkey and the Kurds. It's going to be very interesting to see how the United States will handle this conflict. Recently they sent troops to the border between Turkey and Rojava to "protect the Kurds".[3]

Sources:
[1]: http://www.telegraph.co.uk/news/wor...pos-children-pay-the-price-of-Syrias-war.html
[2]: https://now.mmedia.me/lb/en/NewsRep...ordered-to-not-attack-regime-held-town-report
[3]: https://mobile.twitter.com/Dr_Partizan/status/857969469599121408

 

By Kurds I mean the ethnic Kurds, largelt represented by YPG. Although SDF consists for the main part of YPG, they are an amalgamation of a number of factions. If you look closely, the USA has trodden a fine line to provide support to YPG only vicariously, by supplying the non-YPG factions within the SDF.
Russian support for Kurdish autonomy is a bold statement that the USA is reluctant to match, with potential undesirable (from USA view) repercussions in Iraq and NATO Turkey.