Yes. Weapons hitting places deep inside Russia that haven't been hit before is escalation. Whether one favors the act or not isn't how a step is considered as escalation. Now the Russians might or might not take steps that the other side considers escalation.
Ukraine has been hitting targets "deep" inside Russia for a long time now - further than ATACMS or the export Storm Shadow/SCALP-EG can reach. Whether Ukraine use their own weapons or those purchased/gifted from others seems irrelevant. This is Russia saying "we can hit you with weapons provided by other nations, but you cannot be allowed to hit us likewise" - it's pathetic.
As for what Russia may do, they've been told publicly and privately by multiple nations: from the U.S., UK, and France, even China and India to wind their necks in with regard any nuclear escalation. However, they are very adept at asymmetric responses, and Putin has already said he would consider arming groups with anti-"western" sympathies - he probably already has.
Earlier hits were using Ukrainian drones, while the Atacms are reported as needing to be programmed by US military to hit the targets. So while it is Ukraine that supposedly fires them, it is the americans who will reportedly get them to their intended targets. I don't think there is any moral debate in Ukraine hitting Russia with missiles. After all it is a war fought by Russia against an Ukraine which has Nato proxy support. But it is an escalation nevertheless.
It is now up to Russia on how to respond. And as you noted, one scenario being talked about, at least in social media, is some groups houthis, hezbollah or others getting Russian missiles and those being fired at western targets, ships or others. And I assume it would be Russian military who would control the targetting in that case depending on the missiles used. Or the Russians don't go for direct escalation with the intent of not jeopardizing the chances of Trump ending support to Ukraine in few months from now.
But either way Russia's deterrence against Nato has been challenged yet again, and the chances of escalations and counter-escalations going out of hand remains a more nearer scary possibility in the unfolding scenario in process.
We need to make clear we have the cards. Russia invited us to slaughter the forces sent in in 2014 by making them deniable. They backed down when Turkey downed one of their jets. The instant they feel real force they back down.
