Why does Dictation keep stopping working in pages and notes?

Dictation abhors a vacuum. If you pause in your speaking to contemplate what you are going to say next, dictation times out because it is sending your spoken words to Apple servers.

The macOS and iOS operating systems are not the same owing to their hardware platforms and this may have a direct bearing on how dictation is implemented on either. Unlike your iPhone 15, an M1 Mac mini has no microphone to capture your spoken words and requires a premium third-party microphone to approach the capability of the iPhone 15's multiple, 4K Dolby Vision recording microphones. It also has improved processing power over your M1 mini.

I stopped tormenting myself with Mac dictation long ago as it was exasperating. I cannot definitively state that Apple has improved dictation. One's results improve when using a proper third-party microphone, speaking in a clear voice, understanding dictation command syntax, and avoiding pauses in the dictation process. Even that may be inadequate.