Ukraine had signed the Minsk agreements only to buy time to build their military to NATO standards. Petro Poroshenko and Angela Merkel have admitted as much. With the US promised them backing they believed that they could be victorious even if Russia intervened.
Armed with this information they were planning and preparing to take back Donbass by force. OSCE data shows increased activity and casualties on the Donbass side in the days leading up to the invasion. Remember how Ukraine was constantly pleading for a no-fly zone? They had likely been counting on it (false promises), that the US and NATO would jump in and give them the upper hand.
At this point Russia couldn't really have let the ethnic Russians there lose and die in large numbers with the remainders getting assimilated through Ukrainization as this would've been quite a bad look back home (Russia has always protected ethnic Russians in other countries) and so it was more or less forced to act. The US knew this and still pushed for it. It was certainly not an unprovoked aggression. Remember Euromaidan where it was portrayed as all of Ukraine protesting? It was actually closer to a 50/50 split (population vote) between EU and the Russian customs union in late 2013.
As for Russia losing much? Compared to Ukraine and Europe (who are the big losers here, Ukraine for obvious reasons and Europe financially and industrially) not so much at all. Since 2014, when the sanctions actually made a decent impact, Russia had spent all this time hardening their economy. Living standards of Russians hasn't really changed, aside from some foreign products that aren't available anymore and many already have Russian replacements. They have managed to switch their exports towards Asia and India (and actually made more profits than before). Sure there are things that will take time to adapt and will be costly in the long run but still nothing compared to the problems Europe is facing, barely managing to fill up its gas reserves for this winter.