Replace deprecated `on_init_end` callback in PL App Template

[awaelchli]

Proposed refactor

Replace the deprecated usage with an alternative to collect init args.

Motivation

The PL App Template is using deprecated API that will be removed in 1.8 (#14867) and the new version of Trainer will not be compatible with the template. To be compatible with the newest version of Trainer, the code needs to be updated.

https://github.com/Lightning-AI/lightning/blob/047d7088f4366e68516d017f6e2b81f61bdef13a/src/lightning_app/cli/pl-app-template/core/callbacks.py#L251-L259

Pitch

Options

A) Inject a function through the Tracer to inspect the args
B) Patch the Trainer init with a wrapper

In both approaches we would insert the existing logic for collecting the local argument values.

Additional context

Raised in #14867

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