Russia didn’t conquer Scandinavia, because it would have been a nightmare. The moment the Russia behaved like they would conquer Scandinavia, Denmark and Sweden would have joined in a common alliance, and UK and France would likely have funded that alliances. This would pretty much have removed any ability to invade Scandinavia through naval means, which meant that a Russian invasion had to be through Lapland. So Russia needed to have a army which could defeat the Danish and Swedish one (plus all the mercenaries they could hire with British and French money) walk through a thousand kilometer of wasteland, while the Danish-Swedish forces which would harass the Russians could be supplied from the sea.
Alternative they could try to invade Denmark through North Germany, which run into the problem that even if they do that, much of Denmark lies on islands.
So in short Russia didn’t do it, because even if it (and it’s a big if) was possible, it was really not worth the resources they had to throw after it.
If people want a Scandinavian Russia, a personal union makes more sense. A single different marriage would enable it. Let Queen Louise of Denmark die in 1710, and Frederik IV accept Peter I suggestion to marry his daughter Anna Petrovna to Christian VI of Denmark, in which case their son would be a potential heir to the Russian throne. While Frederik was religious rigid, I think the idea of his becoming Zar would be worth letting him convert to Orthodoxy, likely with a deal the Danish Lutheran State Church, that Denmark and a Norway would stay forever Lutheran. If this doesn’t result in a major succession war, it’s pretty easy for a Russian-Danish alliance to take over Sweden in this period.