Put the barbecue on the outside edge of the deck so their back is to the window?

When someone says “short of” something, that something is usually the more cost prohibitive/complicated/extreme option that exists, which, in this case, might be relocating or removing the window (even the bathroom itself!) or redesigning the deck. A window treatment is the exact opposite! So, why the aversion to the obvious, cheapest, least-complicated choice? Do you hate window treatments in general?

Put in a obscuring glass treatment, like peel and stick frosting. Make or get a real or faux stained glass to put in that window.

Build a large screen outside the window- or build a big trellis and grow it in heavy with something that climbs to cover the window. Maybe cover the window with a cooking accessory rack.

Functional indoor or outdoor shutters...

Move the BBQ so you aren't looking in the window. Build the deck so it isn't in front of the window.

A better design is the first step.

get the window glass replaced with something textured or frosted. depending on what shape your window is, they might even be able to replace just the glass and not the whole frame. if you can't afford that, privacy film is very inexpensive. wayfair and amazon have a ton of options.

Obscuring the glass or a window treatment that covers only the bottom two rows of glass, might be enough but still allow the light. Interesting that a small bathroom window lets a lot of light in to the house.

Frost the windows!

If the interior is really so dark that the light coming from that tiny window is all that’s keeping it from feeling like a cave, I think adding more lighting would be a very worthwhile expenditure, regardless of how you may or may not decide to deal with the window. Since it appears that the only thing above that area is attic space, I highly recommend that some of that light comes in the way of skylights.

Cute house!

Yes just frost the glass.

How about forgetting the deck and doing great patio and landscaping? I MUCH prefer the grounded feel to a patio vs a deck.... and you're yard and proximity to other homes makes a patio seem more private / nestled below a fence line.

My deck extends under the bathroom window just like yours. I put on a peel and stick rice paper look. Obscures the view but let’s the light in.

The solution is not that complicated. Add a window covering -- curtain, blinds, shutter, whatever you prefer - and leave the covering open unless and until you have people in the backyard. I mean, really, most families don't have folks in their backyards 24/7, so it's no big deal to just close the curtain or lower the blinds when you're using the backyard.

I pull the blinds when I have company. Or I use the guest bathroom along with everyone else.