Yes to removing the current shrubs. Might suggest a rounded shrub whose shape can be maintained by periodic trimming. I golden mop might work rather well.

I’m a gardener and love more planting space so I would pull the shrubs and design the bed to cover the entire space between the house and the paver walkway. There’s various ways to do this, but my favorite is to mow the grass there as short as possible and cover with layers of wet cardboard and then 4” of natural mulch. Earthworms love cardboard and they’ll make the dirt wonderful and pliable.

I’m impatient so I plant right away, cutting small holes in the cardboard for my plants. There’s no way to advise you on specific plants because we don’t know if you live in Maine or Alabama or Texas or Wyoming.

You could make a lovely shade garden by removing the grass between the two beds and making one large bed from the front of the patio to the house. Your stepping stones would go through the garden, and you'd use mulch instead of grass between the stones. A little garden there would really soften the area between the two brick houses. Take all the grass out that's between the houses.

You'd use a medium sized shrub with an open structure or a dwarf conifer under the window and plant ornamental grasses in front of it to soften the edge of the path. My favorite for shade/part sun is golden hakone grass (Japanese forest grass).

Here's a simple example of flagstones through a mulched garden.

A more developed design with gravel between flagstones.

Hakone grass lining a walkway.

I suggest azalea bushes. There are pics below from Pinterest. Get some color in there.

I would leave the current box hedge but cut it down to about 10 inches. Thereafter I'd keep it clipped at about a foot high. Behind the box I'd put a single, white, evergreen azalea or rhododendron with a mature height the same as the window sill.

I'd also have a proper path that you can wheel a barrow along rather than the stepping stones and hard to maintain grass.

I agree with Norwood Architects, a Dwarf Gold Mop Cypress for year-round interest. It should only get about 3-4 feet tall and wide and won't block your window. You could fill in the outer edge with annuals or a ground cover.

I doubt it gets much sun in that corner.