docs: extend extension documentation

[jvanstraten]

• Coin the term "core extensions" and describe why they (and extensions in general) exist.
• Document guidelines from #251 and #307.
• Document common options in core extensions (#254).
• Better integrate the function documentation generator output into the website.

~~This depends on #309 (its commit as initially proposed is included in the history here) so I've marked this as draft for now. There's also a hidden conflict with #302, since this documents the option that a change is being proposed for there. I'll rebase/update when both of those are merged.~~