In a text such as
「『捨てる 』技術」 how much space is expected between the first two characters in typography, if any?
When there is no additional constraints imposed by kinsoku or full-justification, this is how
「『捨てる』技術」 is typically typeset (produced by Adobe InDesign 2020, font: 小塚明朝 Pr6N, all characters are zenkaku):
That is, brackets are rendered like zenkaku or hankaku depending on the surrounding characters/symbols. In other words, the built-in space is usually 50% but it sometimes becomes 0% (or somewhere between 0% and 50% when kinsoku is relevant).
Note that this is for main body text. In posters, book covers and such, you may want even narrower spaces, especially between
技. Also note that detailed rules vary from publisher to publisher. The InDesign's settings dialog looks like this.
Typically in Japanese, you don't really encounter spaces, unless you are parsing for someone who is struggling to read. The only exception is romaji, which is typically only used by foreign Japanese learners.
The 「」 and 『』 characters, along with a few others like square brackets, round brackets and parenthesis, have a space built into the character. This is because the actual character is half-width, meaning it doesn't take a full square like other Japanese characters. Because of this, when typing in full-width modes, you'll notice that the characters have a built in space wither before or after the character in question. The same also applies to the sentence final '。' character, as you can see by the single quote positioning.
So to the best of my knowledge the answer is that you usually won't use spaces, as they are typically built into the system. There may be stylistic reasons to add spaces, but it isn't required by the language.