My default out of the box way to approach this would be something straightforward like a BERT-alike encoder to embed each target sentence in a FAISS index (hell, podcasts aren't long -- it could be brute force lookup, I suppose) or similar, with the same encoder running on the queries.
Something I've been playing with is Flan-T5 (https://huggingface.co/docs/transformers/model_doc/flan-t5), which has really strong out of the box question answering capabilities. I could see chunking in larger blocks and using the blocks as a context passage and the query as a question-oriented prompt. I've run some fine-tuning experiments with this setup for text generation (e.g. write me a summary of Huberman's key takes on dopamine) and find that the Flan-T5 model forgets a lot of its other capabilities when subject to fine tuning.
In any event, understand if you're not inclined to share, but love talking shop on this stuff.