My font has curly single- and double-quotes (confirmed in Caps and by manually inspecting the .fnt file). But when I render those characters in strings (Lua), they are replaced onscreen by ASCII straight quotes.
‘ ’ “ ” ...render as...
' ' " "
ASCII ` backtick is not affected.
Other non-ASCII characters render just fine—for example:
× • … © and the various Playdate button glyphs.
(For the heck of it, I tried escaping curly quotes with \ but it didn't help. That would be acceptable, though, if it helps you implement them!)