Braid's search is certainly something that can be improved. In practice, it's actually pretty rare to have to fish for something in the archives, because you tend to keep relevant conversations open until you're done with them. (We also have "starring", like in Gmail, so that you can move conversations out of your inbox, but still keep them easily accessible).
On a day-to-day, a good "search" experience might actually be more relevant for slicing-and-dicing through your Inbox (ie. triaging the firehose of daily messages), rather than digging up old messages.
The way we use Slack at work, most conversations spin out to threads, and there is no jumbling up. If people in your organization aren't disciplined enough for Slack threads, I can't imagine that those people would be disciplined enough for keeping conversations separate either.
I think a conversation-first comms platform is a brilliant idea (though not sure this fits Braid). Instead of channels that can languish and/or have multiple conversations all jumbled up, you get a new window for a new conversation, even if it's the same group of people. With easy searching and archiving I think it could be great. If it isn't a thing in Braid or wherever else maybe I should shut my mouth and start a product