Creating a multi-paragraph blockquote in WordPress's Text Editor is simple - deceptively so!
There's an HTML element called <blockquote> which is really useful for marking up quotations that are long enough to warrant their own section (rather than being inline as part of a regular paragraph).
Most websites will then apply a specific blockquote style, which commonly includes an indent. Sometimes large, stylised opening and/or closing quotation marks are also included as graphical elements.
By way of example, here's the Technically Product blockquote style:
This is a made-up blockquote just to illustrate this website's blockquote style, which has deliberately been kept simple.
Note the lack of giant quotation marks!
As in my example, it's absolutely fine for a blockquote itself to consist of more than one paragraph. In HTML, the markup would look like this:
<p>This is paragraph 1</p>
<p>This is paragraph 2</p>
In WordPress' Text Editor (now part of the Classic Editor), things are a bit different. Leaving an empty line between two lines will automatically convert them into paragraphs, so the markup looks like this - note the absence of any <p> tags:
<blockquote>This is paragraph 1
This is paragraph 2</blockquote>
And for the sake of completeness: if you are using the Visual Editor, or indeed a Classic Edit block within the new Block Editor (the thing that was until recently called Gutenberg), you will find the relevant option under the 'Formats' dropdown menu.
Just highlight the paragaph/s you want to form your blockquote, and then select Formats>Blocks>Blockquote.