Have you considered a victorian edge?

https://beyondbehnkes.com/how-to-create-natural-edging/

Weed grasses are seldom intimidated by any groundcovers. I think you are misleading yourself if you think planting a groundcover is going to keep grass weeds at bay in your flower beds.

in theory it would be bushy, mid size, clumping perenneials like Alchemilla mollis or Geranium macrorrhizum...

My dad used to have those kind of plants along the lawn i our tiny garden when I was a kid, seemed to work

fast forward several decades, I keep trying this approach and regularly spend large amount of time weeding out runner-grasses and weeds out of my perennials whilest bit by bit adding some kind of edging stones

(I guess, my late dad did some regular, low key, permanent weeding around the edges)