I have not achieved this in my own garden, but I like the look of plants being the edging or border.
I am going to use the cheap plastic edging, but want to hide it by growing plants just inside it.
Where there is no "lawn" then I like just a gravel or mulch path, and a natural transition to the garden beds.
Gravel is a good place to grow some wildflowers and other plants. We used to have a gravel parking patch,
and I am sorry that I loaded organic matter over it. The parking patch was ideal for growing Iceland poppy and
phacelia campanularia.
One of the reasons that borders or edgings are required:-- is to let visitors know where they can walk.
Plastic box planters can be used as borders too. If they are filled with lighter potting soil, they can be moved and the grass mowed to the bed, and then they can be positioned over the line of the bed.
My late DH was a finishing carpenter, and he liked to lay everything out using his right angle tool!
To overcome the lack of curves in garden beds---I would plant some plants so they would grow out over the straight edges. That way I obtained some curvature to the rectangular beds.