These are not strictly a result of targeting browsers for desktop applications, it's strictly down to design decisions that have nothing to do with how its implemented. I've seen plenty of wonky desktop/native applications that took way too many liberties with design whimsy that end up being a worse user experience than any webpage.
I also can't complain about Slack being slow because it doesn't seem slow to me and I'm part of a very large organization. I also use VS Code which is based on browser tech, and it's working really well. And I love that VS Code also works in the web applications I create. YMMV.
It's not "strictly" down to this; even if you want to implement interfaces that fit in with native ones, web browsers simply don't expose many native features via the DOM/CSS. It's a question of actual capabilities, not of this hypothetical design process that doesn't care about native integration.
(Of course, there will always be terrible native interfaces. Arguably Apple is the worst offender here!)
Have you tried using a different theme?
Compared to what? I honestly don't know what other people consider state of the art interfaces if native apps are excluded.