Go to https://wiki.lineageos.org if you want to install and/or compile for a phone.
wiki.lineageos.org has specific install instructions for every phone/device they support, I have no idea why you would choose to follow anything else.
just as an example, for the Nintendo switch v2(devices built after the homebrew method was patched) can be found at:
https://wiki.lineageos.org/devices/nx_tab/install/variant2/
There's an install guide for almost every android capable device for the last decade on the wiki!
Ironically, the Switch 2 page you linked on their wiki mentions a few different install methods and locations and goes on to say about one of those:
> if you wish to install Android to the eMMC, you will need to consult external resources
So it seems that there are indeed cases where you have to follow other things than the guides in the wiki, even for supported devices.
There are a lot of phones missing from there though.
and then maybe ubuntu touch: https://www.ubuntu-touch.io/
edit: list of supported lineagos devices (would have been crucial to note in the OP that only certain devices are supported; some have "unofficial" third party support as well, not listed on this link): https://wiki.lineageos.org/devices/
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.
I'm not saying yours works when it doesn't, but there may be something else going on.
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 don't have it with me, by Play store says that it is incompatible with my device.
Google searches indicated that this is a common problem.
I am aware that the keyboard can be changed.
The question is why I have to change them, when the Lineage versions are open source?
Lineage always presents rooted ADB in the developer options; it is "pre-rooted" for you.
In other words, just like Google.
I switched to Graphene with my new phone. It includes SeedVault which is unable to backup most of my apps and ADB backup works with even fewer (deprecated by Google). So only things I could sort of backup were apps that had their own config/data export options. The stupid, "we know best" restrictions from being able to copy between user profiles also made backup and restoring a PITA (upstream android stupidity, not Graphene specific) It was a few days later before I was back to where I was before having to restore stock OS to get a warranty repair (GrapheneOS does not include repair mode or some such thing that the Google service place required). If I was still on a rooted phone, it would have taken a few minutes to restore everything.
That said, for a user who says "I want a simple easy to use replacement for google captured android", I don't think rooting is likely a concern, so taking the more polished GOS is probably desirable.
[0] I don't have a non-magisk LOS phone to check, but I think stock LOS includes an option in developer settings to allow root for adb. This is mostly not what people mean when they talk about root access, but it's a form of root access.
I find it easier to install, and the fact that you can run google play services in a sandbox, is a great safety blanket.