You are not technically editing the PDF with Preview. You are adding an annotation layer to the underlying PDF text content.
You will need to re-install the font into your local Fonts folder (/Users/yourname/Library/Fonts) so operating system updates/upgrades do not remove the font in the future. The font would then need to be activated in Font Book, and then it should be available to Preview's A˅ text markup tool.
In my Font Book, I searched for just the word Hanzi and got two entries for HanziPen SC, and HanziPen TC. Both are OpenType PostScript fonts, that are not installed. However, if you right-click on the HanziPen SC font name, there is a menu item to Download the font. Do that for each Hanzi SC and TC family. You may still need to activate them in Font Book. Then, they should become available to you in Preview when you next launch it.