"seize what they can of our military equipment"
The United States would absolutely obliterate Europe in that situation and a Russia/USA alliance would be cemented within hours (edit: and by this I mean a full military alliance and coordinated attacks and land divvied up). If Europe tries to seize or attack any USA assets it would be catastrophic.
Europe needs to rearm, start building a stronger European defense industry (while hopefully putting up strong guard rails), and should probably peacefully push American troops out.
Europe can probably defend against Russia on its own right now. If they're a bit short of that capability, they can reach it relatively quickly. They are many years away from being able to attack the USA without it going badly for them.
I'm sure that several prominent politicians have been putting together teams to run campaigns but the GOP candidates probably mostly wanted to avoid any official announcements or major actions until Mitch made it official. Now the gate is open and the race is on.