If you did want to be able to remove the Pico (while using the 0.05" pins on the end) then you can get surface mount half-height sockets where the pins stick through holes in the PCB itself.
Picture below but I don't know any part number I'm afraid...
You may also be able to get 0.05"/1.27mm 'stackable' sockets, which would give you enough extra height.
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If you did want to be able to remove the Pico (while using the 0.05" pins on the end) then you can get surface mount half-height sockets where the pins stick through holes in the PCB itself.
Picture below but I don't know any part number I'm afraid...
You may also be able to get 0.05"/1.27mm 'stackable' sockets, which would give you enough extra height.
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