Hope it's not going off topic too much but the same ESR issue affects JFETs.
Most people consider a JFET to have many mega ohms input Rp in parallel with maybe 5pF Cp and assume this model holds up into RF.
But a better model for the JFET at RF is maybe 7 ohms Rs in series with 5pF Cs. Even this crude series model will give a fairly decent curve fit with the admittance curves given on the JFET datasheet. OK, you might have to tweak the Rs and the Cs to suit a particular JFET but one fixed value of Rs and Cs will model the small signal input impedance quite well up into V/UHF. The traditional Rp and Cp model will be completely unrealistic by comparison.
So it's worthwhile looking up the input circuit for each scope model to try and predict how much the input ESR will affect the loading of a circuit by 29MHz or so. A lo of scopes are going to look similar to the Tek 465 with Rs of maybe 40R and Cs of 20pF. I think my old Tek TDS2012 is fairly similar and my old Tek 585 was somewhere in this ballpark but I can't remember. I have a couple of classic 100MHz Hameg scopes under the stairs and I can measure these but it won't be for a day or two.
There are various series to parallel impedance converters online so maybe have a play with seeing what happens to 40R in series with 21pF by 30MHz. The equivalent Rp will be about 1600 ohms! At high power this will get hot and also 1600R in parallel with 50R means about 48.5R so that is a hidden 3% error that will affect any power prediction based on V^2/R.
https://www.daycounter.com/Calculato...lculator.phtml