I’ve been using Debian as my main server OS for a long time, but yeah I’ve started using Alpine for lightweight hosts for a single app/docker lately. Especially on proxmox with the pve-helper-scripts you can spin up an Alpine container or VM with Docker in a few seconds.
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.