How can I export my messages to a zipped file with images intact?

Natively, export of Messages from iPadOS/iOS isn’t possible. Some third-part messaging Apps have an export function, otherwise, you’ll need to use a third-party application installed on a PC or Mac.

Here is one option:

https://imazing.com/guides/how-to-save-iphone-text-messages-sms-and-imessages-to-your-computer

The link is to a totally legitimate commercial software product.