And to answer the OP more directly, what do you give up by using a GrapheneOS (besides being forced to buy a Google device), well, no much since you have the option of installing Google services in a second profile or compartmentalized in your main profile. This, of course, would have your device communicating with Google’s servers, but the info it can collect would mostly restricted. MicroG is potentially more private than creating a Google account (even if an anonymous one), but some claim is less secure too so I leave it as equal.
In conclusion, if you can live without installing Google services or juts just need it so sporadically that you only need to install it in a secondary profile, and you tolerate a Google Pixel go with GrapheneOS option. If, however, you are not a fan at all of having a Pixel, or need to have Google services constantly running, I would consider instead iodéOS, /e/, etc.
Lovely and well researched post… till I see the “tend to be people who also believe that they’re being monitored by the CIA, or that Covid vaccines are implanting mind-control receivers.…”. I find it problematic that both are considered as the same type; there is an incredible abundant evidence that security apparatus of different countries (not necessarily just the CIA that ’ technically’ can only operate in non-Americans) are indeed scrutinizing phone’s data to well beyond what we would consider “the regular suspects”… way beyond! The other, is just people that, while rightly so can be skeptical of government intentions with global mandates, they hide behind that paranoia for their lack of technical and intend knowledge. As the meme says… “we are not the same”.
As for GrapheneOS vs Lineage OS, I am torn. For the majority of people, as of today, LineageOS is just fine… I like that it brings diversity of hardware too since it discourages governments from having to intend to compromise different manufacturers (thing that GOS faults at). Now, more people in GrapheneOS will bring awareness too and more privacy conscious apps. So, for majority of people, do install LineageOS (or their variants), you will be taken good care of… However, for a minority of people, minority but not tiny! you know who you are, you will do better with grapheneOS (hope someone is scrutinizing both GOS and the Pixel hardware though).