I think it looks great as is too.... perhaps permies isn't the best place to look for advice to get a traditional neat and tidy garden.I am quite jealous- the wild flower seed mix I planted this year didn't come up at all!
It kind of reminds me of my favourite garden style- English cottage garden. A google will give you many photos to drool over :). If it was my garden, and I wanted to make it more conventionally 'English cottage', I would work to separate plants out into clumps and maybe mulch around them.A few rocks 'liberated' from a road side can also provide interest and separation, as can trellises and tipis made of sticks or logs. I suspect from the £ symbol you may be in England, and hopefully that's a style your neighbours are familiar with?
I might also add something easy care like a wild or semi wild
rose or climbing rose, rudbeckia, ditch lilies, echinacea, bee balm, cranesbill, or poppies. Our delphinium is glorious right now. Milkweed, butterfly bush, and sedum are other things my bees like. An early flowering edible shrub might even work. I know you specifically said no tulips, but I might consider specie tulips-tiny and glorious, the wildflowers tulips are decended from-, Siberian squill, and crocuses for early season interest. Plants often look more deliberate if they are grouped and clustered and if you mix tall plants and short. It also really helps with weeding long term. I have no idea what was in your mix, but take a look to see what's in it and bloom times- in addition to helping you weed next year, bees and polinators often struggle with finding early season nectar . I might look at something climbing for the
fence next year- I am growing peas and scarlet runners on our front porch rails (yum).