Netdata for me, it reports stats and metrics for VMs and containers too, automatically, and it's easy to install in Proxmox.
yamdwich
My gripe with NC has always been that keeping it up to date is a pain, I love the actual functionality. I'm in the process of migrating my install from a normal install in a TrueNAS Core jail to the containerized version in the Linux version of TrueNAS and that too is a struggle. I'm hoping that the containerized version will be easier to keep up to date, as that seemed to go wrong constantly.
I tried to make Grocy work as a kitchen inventory and shopping tool too but damn, it tries to do way too much detail. I'm sure there are people with enough discipline that it appeals to, but I really felt like it was way too particular and entering/tracking items across areas/brands/types seemed like overkill. Its whole system seems unintuitive to me and I never could get to the point where it seemed natural, so I gave up quickly despite really wanting it to work.
Correct, the discovery process where you add them doesn't actually involve the addon and works fine without it. The addon is just a wrapper for the standalone ESPhome web UI. It's also not the only way to author and flash a config to a device, you can do it from any computer and on the command line.
It's not needed, and you can run it separately standalone if you do want it as well.
I used both, I ended up settling on searxng because Whoogle seemed to be unable to retain my settings. Might be something with my cookie configuration, but searxng has no problem remembering my preferences. If that is not a problem for you then they are comparable; Whoogle is pretty simple to get going and works well, searxng is slightly more complicated to set up (but not that much with docker) but has a ton more features.
Yes, it has a local webui by default. You don't have to connect it to their cloud, though I do because it's free and lets me get notifications if something goes offline.