A quick search has revealed a calculator that provides rotational speed on surface vs latitude. I don’t trust my own maths enough to try and verify it, but I see no reason to doubt that it has been written by somebody with better maths than me, and that it is accurate.
https://www.vcalc.com/wiki/MichaelBartmess/Rotational+Speed+at+LatitudeSo, Baikonur has latitude 45, velocity 735mph
John o’Groats has latitude 59, velocity 535mph
This does indicate a difference of 200mph.
GPS satellites orbit at about 8700mph.
Way out of my depth here, but I would have imagined the earliest part of the flight, while still travelling through dense atmosphere, would be the hardest to sustain acceleration. That might explain why the benefit of equatorial launch is more significant than meets they eye in pure percentage terms?
I’d have thought the other benefit of equatorial launch would be for geo-stationary satellites, which must always be above the equator. By launching at the equator in the first place, you’d avoid having to modify the orbit so much once your satellite is up there. Still just guessing, though; I’m sure there’ll be better informed forums, with properly qualified contributors, if it we wanted the real facts.