After a bit of experimenting, I realized my best bet to carry everything over was to start from scratch. Instead of using the Export Tool, I dragged the whole HTML file into the PWA version and everything carried over properly. Tiddlers, plugins, settings, the whole thing.
$:/favicon.ico is used by default, but you can also further customize the icons part of the app manifest by adding tiddlers with the $:/tags/ManifestIcon tag. type/sizes/purpose fields will be passed through to the manifest.
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