Is there a testing lab that has data showing the (actual) produced pressure of Powder A @ X number of grains ,and the (actual) produced velocity for test projectile
Yes, there are many such as that for the Hodgdon group powders (Ramshot, Accurate, IMR, Hodgdon, Winchester. Go to the Hodgdon Reloading Data Center website, select 6mm ARC as an example, whatever bullet(s) you fancy, likewise powders. Both starting and maximum loads consist of charge weight, MV, Pressure.
These are taken from tests in a barrel whose internal dimensions and the chamber cut in it are compliant with the SAAMI specifications for the cartridge using modern industry standard electronic pressure measuring equipment and methodology. That is why they often bear only a passing resemblance to actual results in factory rifles as the latter often have considerably 'looser' barrels and longer-throated chambers. (Some reloading manuals measure pressures in the SAAMI spec kit, but reshoot the loads in a factory rifle to provide more representative MVs.) Older cartridges often show pressures as C.U.P. (Copper Units of Pressure) not psi as pressures were measured in pre electronic crystal / strain-gauge kit in special pressure barrels with attached cylinders to take a copper cylinder, the amount it was compressed by the chamber pressure being used to calculate what that pressure was.
Many other sources quote the pressures so measured, usually for the maximum charge only, but not all do so.
Where the source puts all loads into columns by MV, eg 2,500 ........ 2,600 ............ 2,700 fps etc and doesn't quote pressure (Hornady and Sierra manuals), the companies have carried out pressure-barrel tests and graphed the centre-line through the data points, reading off what charges are predicted to produce the set MVs with the highest quoted charge set at the level below that which exceeds SAAMI MAP values. This used to be done manually on graph paper, but nowadays the lab technician feeds in the relevant data - cartridge, components used, powder grade and charge weights into a PC program and MVs are automatically transferred from the chronograph and the calculations run there, even building a printer-ready table for the next edition of the reloading manual in at least one bullet company's case as different powders are tested.