Graphene will strongly discourage you from retaining root over your device, while all LineageOS releases present rooted ADB.

I understand that you can forego the final relock of the bootloader and install Magisk into Graphene. How that fares with future OTAs I do not know.

There are other differences that might impact you. The eBay app does not work on Graphene but is functional on Lineage. Graphene's launcher and keyboard are poor compared to Lineage. The Vanadium browser's dark mode is not as good as browsers on Lineage. Pattern lock is not available on Graphene.

Try them both, if you can.

Just tried it out with GrapheneOS on my Pixel 7 and the eBay app works fine.

Generally I think the marketing of GraphenOS is interesting. They are usually positioned as the "Absolute security. No compromises." ROM, but in my personal experience, they are the "It must work. No compromises. Then make the rest as safe as possible"-option, given aspects like using the "real" Google Play Services (if desired), but sandboxed, instead of MicroG or unrestricted Google Play, which pretty much all other ROMs roll with.

I've used the eBay app on various Pixels running GrapheneOS since the Pixel 6 without issue. In the Owner profile, in a secondary profile, in a Private Space in the Owner profile, installed via Play, installed via Aurora.

I'm not saying yours works when it doesn't, but there may be something else going on.

you can easily change the launcher & keyboard to whatever you want on GrapheneOS. About ebay, check https://github.com/GrapheneOS/grapheneos.org/issues/1351

Any idea why any app that works on Lineage would not also work on Graphene, provided you are okay enabling the exploit compatibility toggles where necessary?

I've never rooted my phone for LineageOS (and I have installed it on at least a dozen phones now). The only thing you need to do is unlock the bootloader (which you cannot relock, like with Graphene).