If you want to make the garden feel more secluded, you could make the border full width at the driveway end, giving you a nice big area to plant some shrubs that will grow fairly tall, maybe even a small tree.
Something like this (hope you can make out what I mean from the dodgy drawings (and I'm not sure if that's your house in your 3rd pic or someone else's)
Doncaster, South Yorkshire. Soil type: sandy, well-drained
I have stepping stones so no wading required @ImpatientGardener! You are right, though, we have no idea how much time and cash the OP is prepared to devote to border planting and maintenance or what they intend to plant. We do tend to get a bit carried away...
I would say 1.5m is a good width and the OP’s original instinct was correct. I think with a long stretch of straight border like that, anything less would look a bit mean. With a border in front of the whirlygig as well, the proportions of the lawn will be balanced out, so it won’t look any longer, so definitely worth considering.
Mountainous Northern Catalunya, Spain. Hot summers, cold winters.
I agree with Nollie's suggestion. You already have the paved whirligig area, just make the border L-shaped and create a path through to the next bit of garden. I think the proportions you've marked out with the bits of wood are fine.
"What is hateful to you, do not do to your neighbour".
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I would say 1.5m is a good width and the OP’s original instinct was correct. I think with a long stretch of straight border like that, anything less would look a bit mean. With a border in front of the whirlygig as well, the proportions of the lawn will be balanced out, so it won’t look any longer, so definitely worth considering.