Auto-pasting into whatever application I have open

I find that Monologue often takes about five‑ish seconds to transcribe whatever I've said into text in the application. Sometimes I'll open Claude and be transcribing, intending to paste from Monologue into the Claude chat box, but in the five seconds I'm waiting for Monologue to finish processing, I'll open another application and the transcription will paste into that application instead. Is there a way to have Monologue transcribed to the application that was open when I first started it?