Which version of Session Buddy are you using? Make sure you're on the latest version. Search now filters collections and history, which depending on use case may be easier than using the results dropdown.
With proper search term parsing, metadata queries, and scored results, search is arguably more powerful than it was in v3, but there is definitely room for improvement. Lack of support for quoted search phrases, as you have rightly pointed out, is a good example. Please know that we're aware of the limitations and are committed to continuing to improve search over time.
Do keep in mind that SB v4 was a full rewrite with a hard deadline (due to Chrome deprecations), so some things are not quite the same. We genuinely appreciate your patience while we're working hard to bridge the gaps.
Cheers,
Hans