What about the obvious: a mirror over the pedestal sink and a cabinet with doors above the toilet for storage? Paint wainscoting, it’s cute and the alternative would not improve matters. The light fixture may need to be moved to be centered over the mirror or replaced to go with the style of the mirror and cabinet and new shower. Be consistent with styles and choose everything together.

I would do a recessed mirror cabinet basically the size of whatever was there before. And I would get a small vanity with storage.

You only have room for one mirror over sink. Are you keeping pedestal sink. If you can replace that with small vanity cabinet that would be great.

+1 on recessed medicine cabinet / mirror combo above the sink. Recessed will give you a more minimal look, not take up extra space, I think the frameless one like in my below pics would fit in with any style. And still gives you adequate storage.

You could remove the wainscoting but it will likely be a lot of work to smooth out the walls for paint, especially if it's glued down as there will be leftover adhesive stuck to the walls. I removed some in a small bath once and had to skim coat the entire lower half of the walls.

Plus... the wainscoting seems to match the style of what else you have going on, like the pedestal sink and the shower tile. If you were going for a more modern look I'd say get rid of it but as-is it looks just fine. Just caulk any gaps, sand any imperfections if needed, and give it a nice fresh coat of white paint.

I'd paint the walls a light color. Doesn't have to be white, or even a neutral, but just not too dark. I think small spaces should feel light and airy. Maybe a light blue or light gray.

Might consider changing your light fixture and receptacle covers to white instead of black/oil-rubbed bronze. Generally all the fixtures in a room should be the same finish for visual consistency.

Regarding storage, in addition to replacing the pedestal sink with a slim vanity, you could do floating shelves or recessed shelves next to the mirror.

Another idea aside from centering the light fixture that is above the mirror is to move it to the side of the mirror (better face lighting) and install some overhead recessed lights in the ceiling for fill.

Another mirror option would be to have a LARGE mirror that goes from wall to tub, filling the whole width above the sink and toilet, with a simple wood frame. This would help the room feel larger, but you would sacrifice any storage options on that wall which I'm guessing is a no-go.

Whatever you do for the mirror, I would not do two mirrors, and 16" seems pretty small. Personally I don't think you have room for a round mirror that would be large enough.

Some of these ideas I'm borrowing from my own small bath remodel... it's more of a modern take, but it's only 5'x7' and might give you some ideas of how you can utilize the space and/or storage in a small space to work with.

Some of these pics are WIP before everything was installed.

I recently added this second floating cabinet to the right of the toilet and there will be a shelf between the two for an extra place to set things.