Private guiding is expensive, but when you consider the cost of US lift tickets at Western resorts ($250-ish) without a pass, it's not completely unreasonable - especially with 2 people.
A good list of off-piste Euro areas is
here. Yellow itinerary routes in Switzerland are avalanche controlled but not groomed and can provide a safe off-piste experience. There are some in Austria too.
Private guides cost about the following in the main Euro ski countries:
Italy - 350 Euro
France/Austria - 450 Euro
Switzerland - 450-550 CHF
You can generally do a half day for 3-4 hours for about 50-60% of a day's cost. Sometimes one day is all you need because you can ask the guide about different zones (access, stability) for future skiing or return to what the guide took you on.
Better values are joining a group at some of the larger off-piste meccas like St. Anton, Val d'Isere, or Chamonix which can bring costs to around $100 USD per day depending on whether it is a 6 or 8-hour day. American tipping culture is not in effect so it's often buying a guide lunch or beers afterward - and maybe something extra if you had an exceptional day. (My UK friends made me swear I would not go behind their backs and tip American style). Some Swiss resorts are harder to find freeride groups - Verbier, Zermatt, Engelberg, and Andermatt. Or other French resorts. You need to do research/calls to see if they are putting groups together - not just a simple Google search or ChatGBT query.
I have only done the private guide route with 1-2 persons 3x (Val d'Isere, Chamonix, and Verbier) since I wanted to ski some specific advanced routes. However, mostly I have split a guide with friends (4-6 people) or joined a group/freeride camp: Andermatt, Engelberg, Courmayeur, Chamonix (Aguille di Midi / Les Grands Montets), La Grave, Serre Chevalier, Les Deux Alpes, Arlberg (St. Anton/Zurs/Stuben/Rendl), and Japan (Niseko/Kiroro/Rusutsu).
Guides can generally find unskied areas up to a week after a storm. Some want you to even have touring skis if you are going looking for powder. However, do not expect miracles if it's been a week+ without snowfall. Might want to pass on guided skiing.
Also, you can generally ski some off-piste near the pistes. The Euro resorts are required to keep the pistes safe so generally, some terrain around them is controlled to a certain extent.