Install signal handlers earlier in the startup process

Right now, signal handlers are [installed](https://github.com/elastic/elastic-agent/blob/68e52d042cc28481ab2e882c85f41e3132d6f7b5/internal/pkg/agent/cmd/run.go#L497) asynchronously relative to the coordinator, after all the other setup. If Elastic Agent gets a signal during startup, it'll be terminated ungracefully. The handlers should be as early in the startup process as possible.

The best way to do it is probably to use a context and refactor startup to handle it gracefully.

This caused a test to be flaky here: https://github.com/elastic/elastic-agent/pull/14150. Turns out agent logging `Elastic Agent started` does not mean signal handlers are registered.

Start in internal/pkg/agent/cmd/run.go around the signal-handler installation at line 497, then review the startup flow relative to the coordinator. Use the flaky test context from pull request #14150 to check behavior when a signal arrives during startup. Done means handlers are registered earlier and startup termination is handled gracefully.

Written by the indexing model from the issue text.