fix(server/v2): use only one logger for app and server (backport #22241)

[mergify]

Description

Closes: #22237

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Summary by CodeRabbit

• New Features

  • Enhanced context handling for improved modularity.
  • Updated logging level configuration for the CometBFT server.

• Bug Fixes

  • Improved error handling in command initialization.

• Refactor

  • Simplified server initialization by removing unnecessary parameters.
  • Consistent naming conventions for logging variables.
  • Streamlined command execution flow.

• Chores

  • Removed unused logging imports from various files.

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This is an automatic backport of pull request #22241 done by [Mergify](https://mergify.com).

[mergify]

Cherry-pick of 1f941bb has failed:

On branch mergify/bp/release/v0.52.x/pr-22241
Your branch is up to date with 'origin/release/v0.52.x'.

You are currently cherry-picking commit 1f941bbec.
  (fix conflicts and run "git cherry-pick --continue")
  (use "git cherry-pick --skip" to skip this patch)
  (use "git cherry-pick --abort" to cancel the cherry-pick operation)

Changes to be committed:
	modified:   simapp/v2/simdv2/cmd/commands.go
	modified:   simapp/v2/simdv2/cmd/config.go
	modified:   simapp/v2/simdv2/cmd/testnet.go

Unmerged paths:
  (use "git add/rm <file>..." as appropriate to mark resolution)
	deleted by us:   server/v2/commands.go
	deleted by us:   server/v2/server.go
	deleted by us:   server/v2/server_test.go
	deleted by us:   server/v2/util.go

To fix up this pull request, you can check it out locally. See documentation: https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/reviewing-changes-in-pull-requests/checking-out-pull-requests-locally

[github-actions]

@mergify[bot] your pull request is missing a changelog!