Did people actually talk like they do in Pride and Prejudice?
The dialogue definitely is embellished for better reading.
Austen was innovative in using far more dialogue than contemporaries. Dialogue is pivotal for her stories and is tuned to the character speaking in a very exact way. Dialogue is narrated as people would love to have sounded, and loved to read about.
"Then," observed Elizabeth, "you must comprehend a great deal in your idea of an accomplished woman."
"Yes, I do comprehend a great deal in it."
"Oh! certainly," cried his [Darcy's] faithful assistant [Miss Bingley], "no one can be really esteemed accomplished who does not greatly surpass what is usually met with. A woman must have a thorough knowledge of music, singing, drawing, dancing, and the modern languages, to deserve the word; and besides all this, she must possess a certain something in her air and manner of walking, the tone of her voice, her address and expressions, or the word will be but half-deserved."
"All this she must possess," added Darcy, "and to all this she must yet add something more substantial, in the improvement of her mind by extensive reading."
"I am no longer surprised at your knowing only six accomplished women. I rather wonder now at your knowing any."
– Jane Austen, Pride and Prejudice (1813)
References:
https://www.teachingenglish.org.uk/article/pride-prejudice-art-conversation
https://en.wikipedia.org/wiki/Styles_and_themes_of_Jane_Austen
It's certainly true that a lot of (well-educated) people wrote in that style: not just in novels but in letters to one another, which, even now, tend to be more formal, correct and "flowery" than spoken language. This is partly due to expectations of "how one is supposed to write a letter", but also due to the fact that letters aren't extemporary - one has more time to think about how to compose it.
Since we don't have any recordings of people speaking, books and letters are the main records that we have of how people spoke: there will be some transcripts of people speaking spontaneously, but these may be most commonly taken from legal proceedings, which may not represent a true cross-section of society either.
So, I think that there tends to be an assumption that because people wrote to each other in that style, they walked around having conversations in that style too. That may not be the case at all.