How can one search for some text in one's deleted chat messages?

While there's no stock way to do this, it is possible to write code that downloads all the messages in a room, then goes through the ones which were authored by you and deleted. For those, you could then obtain the message text from each message history page. At that point, you'd have all the text for the messages in that room which were by you, including deleted, but excluding any where the content was overwritten and history was purged. You could do that for every room on the chat server, including deleted rooms, which would give you all the messages by you, except those in private rooms to which you no longer have access (and excluding those messages where the content had been overwritten and history purged). You could then search through the text of the messages.