const conversations = await chrome.storage.local.get({ "chat:conversations": [] });
const messagesObj = {};
for (const conversation of conversations['chat:conversations']) {
    const conversationId = conversation.id;
    const messages = await chrome.storage.local.get({ [`chat:messages:${conversationId}`]: {} });
    messagesObj[conversationId] = messages[`chat:messages:${conversationId}`];
}
console.log(messagesObj);

或者一句获取所有!

chrome.storage.local.get(null, function (data) { console.info (data) });