I have our web.config gettings its appsettings from another .config file in the same folder. We don't use the Serilog appsettings library simply because we already have a bunch of custom flags (disable/enable various modules, auth schemes, etc) so Serilog settings were just another set of flags.
The settings we have include (I've given the descriptive names/purposes)
Customer installation name - this is part of every log's context. It helps to differentiate between multiple installations on the same IIS box. Of course you can use Seq auth tokens for this too.
Default minimum logging level
Use Seq sink?
Address of Seq server
Auth token for Seq server
Use console sink?
Use rolling file sink?
Rolling file name
These settings are read and configured when first setting up the global logger (which is then put into a Windsor container).
We haven't had a need to go crazy with different logging levels for different components in the application although I could see some merit in that down the line (NLog's walkthrough really encourages this sort of thing).
Is that the sort of stuff you were after?