Please add support for Azure Application Insights to use Telemetry

### Feature Summary

Integrate Telemetry support like already available with the Azure Application Insights SDK

### Feature Description

We would like to enhance ALAR (https://github.com/Azure/ALAR) with Telemetry informtion.
The only kind of information we require are 'Logs'. Metrics or Tracing isn't required by ALAR.
The information we intend to log are
- Exceptions (why was ALAR not able to identify a Linux Distro; At what stage got ALAR interrupted and what may have lead to this exception)
- What Distro name and version needs to be recovered by ALAR
- Is ALAR used by 'vm-repair extension? | Used from a CLI environment? (Indication that SELFHELP or vm-repair extension can't be used by a customer) | Used by SELFHELP?
- What action should be performed by ALAR

Especially the SELFHELP scenario gives us a lot of feedback how many support tickets got avoided.

### Use Case

Creating telemetry data by ALAR gives us valuable insights how often ALAR is used . And how many support cases got avoided with the help of it. Also it helps the ALE team to recognize what typ of action got used the most, so our interal training and external docu can be better maintend and improved

### Alternatives

Not aware of an alternative solution

### Additional Context

_No response_

Begin by reviewing ALAR's current entry points and the Azure Application Insights SDK integration requirements; the issue names no files or tests. Done means ALAR emits the requested logs for exceptions, distro recovery, invocation context, and selected actions, while excluding metrics and tracing.

Written by the indexing model from the issue text.