When pasting in from the Character Map (not Paste and Match style) the symbol appears in the correct font but in the wrong size.
I would also like to see a press here to insert button, rather than having to copy and paste. But that last is not essential.
Scrivener just uses the standard Windows Character Map, so I’m afraid this is all handled by the OS. If you have certain characters you use frequently, you might want to try setting up a substitution for them so that typing a specific abbreviation in Scrivener will insert that character. Some are already set up if you just tick the box to enable additional substitutions in the Correction tab of Tools > Options… such as replacing © with ©. Just click the “Edit Substitutions” button to add more.