You can save your work as a PSD file (to preserve the whole structure of the document) using File - Save as PSD. You can also save your file for the distribution on the web (through JPG, PNG, SVG, PDF and other formats) using File - Export As - PNG, JPG etc.
The Save for Web window lets you choose the output format. You can also enter the resolution of the output image. Now, you can already use Photopea to resize images (File - Open, File - Export As - JPG, enter the new size and Save).
When a document was opened from your device, the File - Save option will not work (Photopea is just a website, and it can not rewrite files in your device). You have to use File - Save as PSD instead. But if you opened your file from Google Drive, or as a Smart Object, or from a server (using the API), File - Save will save your file to a correct destination.