Traditionally, paragraphs in speech are rendered like this:
The professor harumphed. "It's not as easy as that. "English grammar is surprisingly complicated. Why, only yesterday..."
That is, only having a closing quotation mark at the end of the block and omitting the ones in paragraphs inside the spoken text.
Is this still a thing these days? Text rendering does change over time --- why, I remember the days when you pluralised numbers with apostrophes ('Personally, I quite like 4's and 5's.') and was quite glad when that went away.
It does look kind of weird, and as a whole I tend to rearrange my prose not to need it (e.g. adding a 'he said' to the first paragraph), but I dislike changing my writing style just because of a text rendering issue. If it's not a thing, what's the current approach?
(Note to mods: I've tagged this with 'grammar' because I can't think of anything more appropriate --- feel free to retag.)