Most “meters” use averaging and also update display digits only if there is trend going above or below certain threshold.
Anyway, one thing to test is powering your whole setup from battery, for example 2x new AA cells to 3.3V.
I have a pretty decent power supply. It never caused any trouble. Why you thing a battery will produce better results?
Battery always source clean power.
Switching psu at 5v through 3.3v voltage regulator not so clean…
Anyway, if your psu is good and you have caps, it’s probably ok.