serilog-extensions-logging VS attributed

ILogger is an abstraction provided by Microsoft. It is not a logging framework, it's a way to standardize code to work on any logging framework. In your actual program you need to actually put the logging provider under that abstraction - Microsoft provides some defaults like a console logger, but generally you want to configure Serilog/NLog/whatever. See: https://github.com/serilog/serilog-extensions-logging

Microsoft.Extensions.Logging is a pipeline that uses Microsoft.Extensions.Logging.Abstractions as its structure. It doesn't actually write logs to anywhere or anything, for that you need a provider. Microsoft offers several providers include Console Output, Windows Events, et al. Serilog is just another provider.

You may need to enable logging, otherwise Activity will be null as described here. Regarding your exception message, you're not doing anything with the exceptionHandlerPathFeature object. The documentation you linked to shows some type checking with the is operator to produce an error.

Have used this package quite a lot: https://github.com/destructurama/attributed

You can use this Serilog extension library to mask any properties containing sensitive info: https://github.com/destructurama/attributed