Well finally got a call back, a 24 x 24 is $3680 + permit cost, a 24x22 is $1760 + permit cost. Upgrading to 2x6 is an extra $1000.
I’ve never figured out how builders bid… Around here (Texas) most seem to just throw out a number per sq ft that has worked for them in the past; I recently had a builder quote $70 - $80 per sq ft for a basic 24x32 stick framed garage. I declined to follow through on that offer...
If you just look at your agreed upon cost for the as planned garage as a basis for additional sq ft, you’d get something like the following:
$19,000 for a 20x22, or 440 sq ft garage that works out to $43.2/sq ft
So, using $43.2 as a basis your upgrades would work out to:
24x22 = 528, i.e. 88 add’l sq ft, 88 x $43.2 = $3,801 additional cost
24x24 = 576, i.e. 136 add’l sq ft, 136 x $43.2 = $5,875 additional cost
However, from an incremental perspective the quote is a bit odd...
88 add’l sq ft for $1,760 which works out to $20 per sq ft
136 add’l sq ft for $3,680 which works out to $27 per sq ft
If you have a decent relationship with your builder, I’d probably recommend just (politely) asking why the increment for one size (22x24) is $20 per sq ft and the other size (24x24) is $27 per sq ft… He may actually have some logical rationale. Generally, I'd expect that a construction for a sticked framed building with dimensions on multiples of 4' to be more cost effective, not less. I also don’t understand the $1,000 increase for 2x6 wall framing and I probably ask why there too. But, I’ve also learned that some times something is more expensive just because someone doesn’t want to do something a certain way...
Anyway, If you go 24’x24’, you may have room for 2 cars and a work bench or cabinets or stuff on one of the side walls and still be able to open doors on either of the 2 cars. 22’ wide would be challenging if you want to open the doors on either of the 2 cars and put stuff on a wall.
If you ever want to do more serious projects in your garage, one of the cars will (most likely) have to move outside. I’d heartily recommend a shed for the stuff you don’t want cluttering the garage.
Attic trusses might also be nice, especially if your roof has a nice steep pitch; I'd guess that your roof pitch might be fairly steep to help with your snow loads...
I have had several houses and all have had different sized garages. 3 houses ago... I had a 22x22 and I didn't get to park any cars in it.

A little over a third of that garage was configured as an office/craft room that I shared with my wife and a closet for bicycle/lawn equipment, while the majority of the space was configured as a motorcycle workshop... BTW, we put a huge amount of junk in the attic under a low pitch hip roof.