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I'd say bifold. If you integrate into cupboards and you have to replace down the line you're limited to the same size + all the laundry room crap is hidden away. Top tip from ours - we have washer and dryer side by side on a raised plinth, with space underneath for 3 baskets similar to this (not readers). Really useful for sorting laundry in a reasonably neat way which might be good if you are walking through there all the time.
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If you did integrated you could make it functional but also look decent maybe - would be easiest to use on the daily.
As for doors to screen the utility space - I do see the logic - bifold's might be annoying unless the hardwear / installation is top notch (cheap rattly janky tracks would piss me off ).
small humans=big washing so when that happens i would posit the doors will be open 95% of the time.
Here's an open E17 laundry zone - bit 'period' style for your place but you get the point.
What's the actual width dim?
Chuck up a photo of the space - or stick a slouchy guy with an untucked Oxford shirt in