Text-based conversations between users with searchable history in Microsoft Teams Free
When using Teams with a personal account (aka. Teams Free), the entire chat history is saved only on the Cloud. You can export your entire chat history from the Cloud and check if the conversation is available there.
https://teams.live.com/dataexport
However, if this conversation is neither available in the app nor on the Web, then it is not likely that it will be available in the export file. When a conversation is deleted, it is also permanently deleted from the Cloud too.