You may want to look into different models that are more accurate and maybe an AEC layer to remove background noise. Or at the very least a RNN de-noiser on the mic channel. Also, you may want to stream audio to the model instead of holding it all in memory and transcribe at the very end as that can potentially allow you to take the app much further than it is now.

I see Claude implemented a very crude upsampling/downsampling algorithm, which is what LLMs usually do when prompted to handle such a problem. But I would suggest restraining the model from implementing DSP processing on their own and instead use battle tested libraries. You can use rubato's FFT Resampler.

Audio processing is genuinely a hard engineering problem, LLMs usually don't get it right. If you decide to get deep into it, the knowledge you'll get is very rewarding.