I am afraid that you won't find a similar infrastructure (well-tended cabins spaced out along the well-marked trek, or at least a well-marked path long enough for multi-day hike) anywhere in Russia. Anywhere that is reasonably picturesque, at least. Casual multi-day hiking is simply not popular enough here; it's generally assumed that people going on long hikes should possess adequate pathfinding skills, set their own tents, find water, etc.
As a foreigner, you'd be better off hiring a guide: there are plenty of companies providing guided tours near Baikal, some of them should have English-speaking guides as well. Not to be too alarmist, but going on your own might be dangerous because Baikal weather may change fast, leaving you stranded behind a flooded creek, mobile coverage may be poor, limiting your ability to call for help, and you can't completely discard a possibility of conflicts with locals, which an experienced guide would mediate.
I've only been personally in Baikal region, but I'd assume that the same applies to Altai (I heard that they offer wonderful horse tours there) and Kamchatka (BEARS!).