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You can edit maps you created by pressing "Browse" button in the Editor launcher menu, just as you select a map to play in the Squirmish menu. There will be map sharing added through the Steam platform (you can claim your Steam key on itch.io, as you bought it).

Thanks for the speedy reply. My issue is that I can select my map by pressing the 'browse' button and it will show me the thumbnail, but then the only buttons I choose after that are the 'New Empty Map' button, which obviously just opens a new empty map, or the 'Start' button, which only allows me to play the map I made, not to edit it.