Are there better&standard way to debug/inspect multiple pin voltages instead of a multmeter? It is rather inefficient.
Some bench multimeters have an input multiplexer option which can be used with GPIB to make measurements of many points under computer control (HP/Keysight used to make this stuff).
If it is just logic levels you are interested in then a logic analyser (or if the design is suitable, JTAG) works anf typically can sample quickly enough to give you timing data.
Sometimes you design in BITE to allow sampling of interesting points with something like a built in ADC.
Checkout DAQs, they offer multiple channels (depending on the model). You can not only get RMS value of the voltage(or current) but can also get the transient data as well.