This feature is now on the backlog. I will update you when we have more details to share.
Work has been done by the team to add support for partial strings. They are continuing to work on improving the experience.
Thank you for your feedback.
We are excited to share that search within a specific chat or channel is now available via Ctrl+F/Cmd+F. To learn more, see: https://support.microsoft.com/office/search-for-messages-and-more-in-teams-4a351520-33f4-42ab-a5ee-5fc0ab88b263.
The ability to search tabs in a chat remains on the backlog. We will share an update as soon as one is available.