Capitalization and punctuation rules for formatted quotations appearing in the middle of the sentence

My question regards situations when the mid-sentence quotation, such as

This is a mid-sentence quotation which stands out by its formatting

, stands out by its formatting.

I understand that this can be rephrased in such a way that the quotation goes to the end. But even in that case there remains the question of writing the final full stop on the following line.

What are the punctuation and capitalization rules for these situations?

It depends on who you are quoting, and for what purpose. In normal writing, it is fair to assume that your source wrote in coherent sentences, which include a capital letter at the beginning and a full stop at the end. So long as this goes within the inverted commas, the sentence does not need re-punctuating. A partial sentence does not (necessarily) require either, but does require an ellipsis [...] to show it is partial. (So if you quote 'everything except the full stop', you end up with 3 dots rather than 1.)

On SE the rules are a little less formal, particularly if you are quoting yourself. If you think your quote would be better without the full stop, go ahead: you presumably won't be misquoting yourself.

The punctuation is the same as for any other clause: you need a comma after the quotation only because you put one after 'such as'.

(PS I use British rules for punctuation and inverted commas: US rules are sometimes different).

There are surprisingly rules for "block quotations", as I think they are called. I found one site, where the author states these rules:

(1) The student removes her quotation marks. (The fact the material is specially indented indicates it is a direct quotation, so the quotation marks are redundant.)
(2) If the student is citing poetry or verse plays, the student removes her slashes for poetic line breaks.
Now the line breaks are indicated by the breaks on the actual page, because she is reproducing the text exactly as it appears on the page.
(3) The normal placement of the final period changes. Now, the final period appears before the parenthetical citation begins.
(4) The margin on the left-hand side of the page is scooted in an extra two tabs (an additional one inch). The margin on the right-hand side of the page remains the same.

Answering your question, the final full stop "appears before the parenthetical citation begins."

Hope that helps:)