The time saving comes in both document retrieval and citations. I haven’t written a manual bibliography since undergrad and every time someone says they do manual bibliographies I really question their sanity! LOL, JK, but not JK. If you submit to various peer review outlets, you likely have to conform to various citation styles. With a citation manager, that’s easy since you just adjust the output of the citations referenced in your article (although sometimes with a few simple mods) and viola, you’re done.
I don’t really like Google Docs for academic writing overall (at least not for finishing and submitting). I think Word works much better across the board with citation managers, including Zotero. I don’t personally like Zotero that much because it is quite limited as technical software (IMO), but it is free and it has a large user base, so I wouldn’t discourage anyone from using it. I don’t want to regurgitate a whole comparison between the two, but this is just my take.
I personally use Bookends. It’s Mac-only and has a one-time user cost, which is great. Customer support is excellent, actually, very responsive from the developers themselves. Good mobile app, simple file structure, iCloud syncing. It’s got a few aesthetic and interface issues, but nothing catastrophic, and besides, you have to remember that citation software is so niche and so hard to develop a business model around (see Mendeley getting gobbled up and abandoned).
Although Endnote is fairly mature as a citation software app, I just totally despise their marketing, their upgrade structure with essentially no new features in literally 10 years, etc. It’s really exploitative.
I also agree with Bluefrog that Devonthink is the way to go on PDF markup, although I find Bookends mobile (on iPad) to also be solid.