The mower is a Murray. The owner manuals for the VRO40-13 HRT, TRX, HRX and TX are all in the manuals section, all with their Murray model numbers as well. However we do not have the workshop manuals, and the maximum engine speed is not stated in the owner manuals.
The issue is that the maximum engine speed depends on two factors: the safe speed for the engine itself, and the speed that gives the maximum allowable blade tip speed of 19,000 feet per minute (a safety requirement, to prevent high speed projectiles being hurled by mower blades). The engine's safe speed will probably be 3,600 rpm, but the mower's safe speed may be a bit lower to comply with the blade speed rule. The Briggs engine manuals do not give maximum engine speeds any more, they refer you to the mower manufacturer's specifications.