Earlier quoted context omitted.
Not really any: popular open-source software, which gets reviewed and rebuilt by many independent people (distro maintainers) has a much lower chance to be hijacked this way.
Oh yes it can. Project owners have sold out before--sometimes without telling anybody. The threat vector is the same. Something you trust gets sold to someone else and it abuses previously acquired trust. Open source doesn't actually fix this specific trust issue. And BTW your browser extension's source is available to peruse locally on your machine after you install it. Surely you did that, right?
Regarding extensions code: indeed, I do read the code of extensions that require some elevated permissions, if these extensions are not otherwise vetted. This is why I avoid installing excessively complicated extensions, unless they ask for minor permissions. Having the list of tabs if no big deal; accessing data in your tabs, even for a particular site, triggers scrutiny.