Enhanced logging for opentelemetry extension startup

[jousby]

Is your feature request related to a problem? Please describe.
There is no existing log statement that marks when the AWS opentelemetry lambda extension has finished starting up and the time taken to start.

Describe the solution you'd like
Currently if you consume the full 'info' level firehose of log statements from the extension it looks something like:

There is an initial log statement:
{"level":"info","ts":1767138850.7595742,"msg":"Launching OpenTelemetry Lambda extension","version":"v0.138.0"}

Then later on there is a log statement that looks like it's saying the OpenTelemetry Lambda extension is done starting but we continue to see log statements arriving for various componenets for several seconds after this:
{"level":"info","ts":1767138851.1722095,"caller":"service@v0.138.0/service.go:245","msg":"Everything is ready. Begin running and processing data.","resource":{"service.instance.id":"2a52aa2e-513b-4392-9876-2a147d3d1ed6","service.name":"otelcol-lambda","service.version":"v0.138.0"}}

Ideally I want to drop all the info level noise (and just listen for WARN/ERROR from the extension) apart from two info log statements recording the extension starting and finished starting (with duration), something like:

• "msg": "OpenTelemetry Lambda AWS Extension Starting..."
• "msg": "OpenTelemetry Lambda AWS Extension Started.", "initDurationMs": 3292

This way i can accurately measure if a change in my collector configuration (new receivers/exporters/processors) and/or an upgrade in the lambda layers has made a material change to the opentelemetry lambda aws extension startup time.

Additional context
Whats mildly confusing here is that both AWS Lambda and the Otel Collector have the concept of extensions. You see the first log stmt which relates to the AWS Lambda extension starting and then you see collector related log statement for collector extensions starting. If you can think of a better way to make it clearer that the start and finish statements related to the aws extension starting and not otel collector extensions starting that would be great.

_{Tip: React with 👍 to help prioritize this issue. Please use comments to provide useful context, avoiding +1 or me too, to help us triage it. Learn more here.}