Sorry for a late reply. As many of you may know we've stopped active development on Stream (classic) and are putting all our effort into making changes for Stream (on SharePoint) which is another way of saying "put your videos into SharePoint, OneDrive, Teams, and Yammer". The current search on Stream (classic) is fairly poor for all the reason in the thread above.
However, if you start putting your videos into SharePoint, OneDrive, Teams, and Yammer those videos will get full real M365 search capabilities. So you can find your videos from any search box in M365.
For Teams meeting recordings where you've enabled Live Transcripts, those transcripts are now searchable to find your meeting recordings in M365 today.
Around April we'll start rolling out the ability to generate a transcript in English for any video uploaded to ODB or SPO. When you do that for a video, that video will also be able to be searched by the words in the transcript.
So we didn't deliver better search on top of Stream (classic) but it's already possible for Stream (on SharePoint), which is uploading your videos to ODB, SPO, Teams, Yammer, etc.