What agricultural zone are you in?

I am in zone 5b.

Groveraxel's advice is solid. You have good lines to the beds but grass would never be good in such shade, and so many nicer options! I think I'd keep the little beds in the corners and plant them with a mic of variegated Hostas and white impatiens.

Vincas are very happy right under a shady tree, no mowing needed. Hostas and ferns would also thrive in the shade, making it look sweet and mysterious.

There's nothing wrong with your garden beds that a nice thick layer of brown mulch can't help! It may take several yards to fill them but just doing that alone is going to make everything looks so much neater and better. Then as suggested plant pachysandra, fern, and hosta. You don't have to fill the bed right away, it could happen over time. I would suggest perhaps making a dedicated walkway through the gate instead of a few stones. I think that would help a lot.

Reputable garden centers no longer sell inpatients because for the past few years they have been infected with a powdery mildew.

Do some research on shade plants that are appropriate for your area. Take a soil sample to your local high-end nursery as they will usually analyze your soil for free. I would suggest adding color with azaleas, they tend to like a more acidic soil which comes with needle dropping.

Hostas, hakannechloa (Japanese forest grass), alchemilla mollis (ladies mantle), pulmonaria (lungwort), Chelone (turtlehead)...there's a long list of perennials that would probably do well. And spring bulbs can also do well in dappled shade.
It would be worth visiting the nicest garden center in town.....if you take a plan (yes, to scale!, with North marked) and some pictures, they'll be very helpful.

Oh, azalea and rhododendron would both be happy in your yard (just choose the more shade loving varieties). They are such happy plants!

Miacomethelady...that is interesting! I live in 3b and we have never had problems with powdery mildew for impatiens....but perhaps it is because our season is so short.

We can not really grow rhododendrons in my zone, it gets too cold, but if you can they are so very spectacular!

This will be the 3rd season. My local nursery said they could only eradicate it by not growing them for a few seasons, so I am not sure if they will be back this year. I just go with Begonia for now.

There are plenty of shade-tolerant shrubs
and plants that thrive in zone 5. Some have beautiful copper-colored foliage that
would compliment your brick house. I see you have a planting bed in front of
the porch, I suggest you create a similar bed on the other side of the path and
make both beds larger so they take up more of the lawn space. Define the edge
of the beds with a lawn edging like this
- This edging is flexible so you can design a curved edge to mirror the shape
of the wall. Once the beds are ready, choose some shrubs and plants for the
beds.

For small shrubs consider Daphne 'Carol
Mackie' which has variegated foliage of green and white with fragrant pink
flowers in the spring, it grows about 3' tall by 4' wide. Other choices are pieris
japonica, azalea and virginia
sweetspire 'Little Henry'. Fern 'Dryopteris Brilliance' and heuchera 'Midas
Touch' both have decorative copper-colored foliage. Flowering plants such as
astilbe, dicentra, hellebore, wood poppy, virginia bluebells and aquilegia grow well
in shade.

In
front of the beds, remove the lawn grass and fill the space with low-growing
ground cover plants. Pachysandra, liriope or ajuga would be ideal. The mature
tree is a great feature and possibly provides some privacy from the busy
sidewalk. I would consult a professional arborist to see if the canopy could be
pruned or thinned - this would allow more sunlight into your garden whilst
keeping the tree. Avoid planting anything under the tree because it's important
not to damage the roots, instead place a 2" layer of wood chip or leaf mulch.
In the area by the fence, add the same ground cover plants that are used to
replace the lawn. This shade garden works well with the natural environment of
your front yard and provides plenty of curb appeal!

Beware that shade around a big tree can also lead to dry soil. Yes hostas and ferns and many other shade plants will thrive there but if it is dry under your large tree you'll need to water constantly or look for shade plants that tolerate dry areas.