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The example you're describing of a voice actor needing to try different voices is Vocal Evolution. As the trope article says, it's very common for the same (voice) actor to modify their vocal delivery over a period of time.
I suppose the voice actor's real difficulties behind the microphone leading to the creation of new in-universe plot elements is Real Life Writes the Plot.
When a show or something of the sort receives an unexpected major or at least noticeable change in it based on something in real life, but the change was given an in-universe explanation
EX: On the F Na F You Tube channel Eth Goes Boom, one of the characters, Toy Bonnie had 3 different voices through the entire series. In real life, Eth had no idea how to voice Toy Bonnie at first, and try to try a few times to find one he liked. But in universe, Toy Bonnie kept changing his voicebox because the kids weren't responding to it. In his case, it led to it's very own storyline that went on for many let's plays
Edited by GxchxFxndoms