chrome.fileBrowserHandler

{
  "name": "My extension",
  ...
  "file_browser_handlers": [
    {
      "id": "upload",
      "default_title": "Save to Gallery", // What the button will display
      "file_filters": [
        "filesystem:*.jpg",  // To match all files, use "filesystem:*.*"
        "filesystem:*.jpeg",
        "filesystem:*.png"
      ]
    }
  ],
  "permissions" : [
    "fileBrowserHandler"
  ],
  "icons": {
    "16": "icon16.png",
    "48": "icon48.png",
    "128": "icon128.png"
  },
  ...
}

chrome.fileBrowserHandler.onExecute.addListener(async (id, details) => {
  if (id !== 'upload') {
    return;  // check if you have multiple file_browser_handlers
  }

  for (const entry of detail.entries) {
    // the FileSystemFileEntry doesn't have a Promise API, wrap in one
    const file = await new Promise((resolve, reject) => {
      entry.file(resolve, reject);
    });
    const buffer = await file.arrayBuffer();
    // do something with buffer
  }
});