Roman not romantic

it doesn't look too shallow for inside mount blinds/shades.

what is the measurement?

all you need is enough room to put a screw through the bracket

Many stand proud of the trim anyway.

Do you need privacy or are you just looking to soften up the window?

Agree with Lyn Nielson that it looks like you have enough room for inside mount. What is the actual measurement?

Wayfair.com has a simple cordless cellular there are lots of options online.

look for inside mount blinds and see what you can find.

INside mount and you need to share the reson for the window coverings that will drive which you need .

You can inside mount shades in very little depth.

• Cellular shades can be mounted with as little as 1 inch window frame depth. Some with as little as 3/4 of an inch depth, however, windows with less than at least 2 inches will not be deep enough to contain the entire cellular shade and a portion will extend past the front edge of the window frame. Honeycomb cell shades are ideal for narrow windows as they require less space to mount than horizontal blinds

We need them for privacy but not to block out light entirely. We

You can’t drill into an Anderson 200/400 series window box. 1 of the 3 windows has a deeper box but the other 2 do not and we’d be drilling into the vinyl.

Roman shades mounted to the outside trim would would fine. They wouldn't sit flush against the window but that's probably okay since you are concerned with privacy not wanting a black out effect. A top rail would be mounted on each side into the trim but below the molding at the top.

Lots of good advice already - I might be tempted to invest in shutters and get something a bit more formal/structured. they are an investment though -