How well is Intel’s Lakefield hybrid architecture supported?
Is Manjaro able to use both the energy-efficient cores and the performance core dynamically depending on workload?
Do the missing instruction sets noticeably impact the performance of the Manjaro desktop itself?
This a kernel thing - check kernel.org - try the search or use the site search in ddg
site:kernel.org intel lakefieldWell, i has been added to the kernel in 2020: x86/cpu: Add Lakefield, Alder Lake and Rocket Lake models to the to I… · torvalds/linux@e00b62f · GitHub
It depends on the kernel and not on the Distribution. So since Intel added it themselves (see above), I would say yes.
No idea 
1 - yes with 5.15 LTS
2 - No , see phoronix & Kernels about this ( coming in 5.17 version )
3 - what “missing instruction sets” are you talking about ?