First, don't go with XPS, since at 2" it would be a Class-II vapor retarder (="vapour barrier" under Canada's code definition). With 6 mil poly on the interior that creates a moisture trap, which puts the window flashing details on the "critical" list for making it
perfect. In construction there's good/better/best, but perfection is really really hard to achieve.
Decide ahead of time whether the windows will be mounted innie (glass roughly co-planer with the sheathing) or outie (roughly coplanar with the siding), since that affects how the window flashing is installed, and
where the housewrap gets installed. If innie, a crinkle type housewrap (eg Tyvek Drainwrap) is strongly recommended, to allow bulk water that gets between the foam & sheathing to fully drain.
Furthermore XPS slowly drops to the same performance of EPS of similar density over time, as it loses it's powerful greenhouse gas HFC blowing agents. XPS is by far the
least green insulation material in common use today:
The greenest foam-over solution that works would be RECLAIMED roofing EPS, which is usually 1.25lbs per cubic foot density "Type VIII" material. At a mean temperature through the foam layer of 40F (appropriate guesstimate for the wintertime averages in your area) it would run about R8.5 @ 2" , R12.75 @ 3", and about 1.5 perms @ 2", almost dropping to about 1 perm @ =3" (which is about as vapor-open as 1" of XPS), which is reasonably sufficient seasonal drying capacity.
The next-greenest approach (that's still affordable) that works would be virgin-stock Type-VIII EPS.
A 2x4/R11 wall runs about R9- R10 "whole assembly" after factoring in the thermal bridging of the framing, and the R-values of the wallboard, sheathing, siding & air films, etc, so even 2" of exterior foam would be nearly doubling the performance of the wall assembly. Before putting up the foam it's worth detailing the sheathing as the primary air barrier using polyurethane caulks &/or sheathing tapes, where appropriate. (With a rollered-on layer of latex primer spanning the seams even housewrap tape works on plywood & OSB).
Vinyl siding needs no rainscreen- it's inherently back ventilated, but it can't be long-nailed through 3" of foam. Using 1x4 furring through screwed with pancake head timber screws long enough to penetrate the studs by 1.5" is the common approach, but you may want to
review this older blog piece before deciding your approach.