The Picoscope details I have seen show an integrated CMOS transimpedance buffer intended for DSOs from TI that by itself has 100 times the noise of a discrete front end at low frequencies. I mean literally 1000nV/SqrtHz where a discrete design could be 10nV/SqrtHz.
So a broadband RMS noise of 125.7uV over 200MHz does not surprise me at all and that is about 5 times worse than my 40+ year old 200MHz analog oscilloscopes.
3000/5000 series ADA4817-1 (4nV), recent series of scopes. Obsolete versions (early 2000's) employed discrete jfet front ends.
2000 series ADA4891-1 (9nV) or AD8065 (7nv) (25MHz versions)
4000 series ADA4891-1 (8 channel scope) and AD8065 on older 20MHz scopes and 4817 on 16bit scope
6000 series BF998 mosfet (~6nV, obsolete device), 6404 is ~12nv due to attenuator configuration
Either Analog Devices parts or discrete jfet/mosfets. The ADA4891 measures closer to 12nV due to 1/f contribution.
I used to design scopes at Pico and wanted to clear up this misinformation, noise is a critical scope spec and we'd use the best parts whenever possible.