For all other fonts, Photopea allows you to open them (TTF or OTF files) the same way you open any other file (File - Open, or drag-and-drop). They will be added to the end of the font list and used, when some type layer needs them.

From the documentation. Doesn't work?

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I did try the feature, but it doesn’t render correctly, at least not for me.

Meh, I would say you try and convert/get the font in a web friendly format before importing. WOFF (first version without compression) seems to be supported or OTF