[public-api] Cleanup logging middleware

[easyCZ]

Description

• Drops auth headers
• Reduces accidental double log
• Does not include body in fields

Related Issue(s)

Fixes #

How to test

Release Notes

NONE

Documentation

Build Options:

• /werft with-werft
  Run the build with werft instead of GHA
• leeway-no-cache
• /werft no-test
  Run Leeway with --dont-test

Publish Options

• /werft publish-to-npm
• /werft publish-to-jb-marketplace

Installer Options

• with-ee-license
• with-dedicated-emulation
• with-ws-manager-mk2
• workspace-feature-flags
  Add desired feature flags to the end of the line above, space separated

Preview Environment Options:

• /werft with-local-preview
  If enabled this will build install/preview
• /werft with-preview
• /werft with-large-vm
• /werft with-gce-vm
  If enabled this will create the environment on GCE infra
• /werft with-integration-tests=all
  Valid options are all, workspace, webapp, ide, jetbrains, vscode, ssh

[geropl]

Code LGTM!