[Docs Request] Add examples for logging to other logging providers.

#### What problem would the feature you're requesting solve? Please describe.
The current documentation is lacking (or hidden?) with respect to logging in an Azure function to _other_ providers, like `Seq` or `Splunk` or `Sentry` or `RayGun` or .

Logging can either be:
- non error messages. Like warnings or just some information
- error messages / exceptions.

#### Describe the solution you'd like
The documentation to be updated to include a sample to or two for handling:
- Log messages
- Error messages / exceptions

and these examples can go to an external provider, like Seq or Sentry. The examples should also highlight going to AI and not going to AI.
e.g. 1: I just want to log errors to Sentry.
e.g. 2: I would like to log errors to Sentry and all data to AI.
e.g. 3: I would like to log errors to Sentry, logging messages to Seq and finally all data also goes to AI.

#### Describe alternatives you've considered
None. Just trying to get Seq / serilog to work. not having too much luck.

No files or tests are identified in the issue. Start by locating the Azure Functions logging documentation and existing Console/Application Insights examples, then determine how external providers and routing combinations are currently supported. Done means adding one or two clear examples covering ordinary messages, errors, and the requested combinations with and without Application Insights.

Written by the indexing model from the issue text.