chore: don't use KonnectClient in ClientsProvider

[czeslavo]

What this PR does / why we need it:

Stop using KonnectClient in the clients' provider. Make konnect.ConfigSynchronizer create one using a factory on its startup instead. Also:

• moves tests related to Konnect-specific behavior to konnect.ConfigSynchronizer.
• moves the call to deckgen.ToDeckContent from KongClient to konnect.ConfigSynchronizer as it may reach out to Konnect APIs while for plugins schemas, and we don't want to spend time on Konnect-related stuff in the critical path

Which issue this PR fixes:

Part of #6340.

[codecov]

Codecov Report

Attention: Patch coverage is 62.29508% with 69 lines in your changes missing coverage. Please review.

Project coverage is 76.8%. Comparing base (40d909f) to head (e9d2fb5).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
internal/manager/run.go	0.0%	23 Missing ⚠️
internal/konnect/config_synchronizer.go	81.5%	17 Missing and 2 partials ⚠️
internal/adminapi/konnect.go	0.0%	14 Missing ⚠️
internal/manager/setup.go	0.0%	13 Missing ⚠️

Additional details and impacted files

@@          Coverage Diff          @@
##            main   #6885   +/-   ##
=====================================
  Coverage   76.7%   76.8%           
=====================================
  Files        214     214           
  Lines      25139   25170   +31     
=====================================
+ Hits       19299   19338   +39     
+ Misses      4825    4820    -5     
+ Partials    1015    1012    -3     

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[team-k8s-bot]

E2E (targeted) tests with KIND-based clusters were started at https://github.com/Kong/kubernetes-ingress-controller/actions/runs/12650457940

[team-k8s-bot]

E2E (targeted) tests with KIND-based clusters were started at https://github.com/Kong/kubernetes-ingress-controller/actions/runs/12651092822

[team-k8s-bot]

E2E (targeted) tests with KIND-based clusters were started at https://github.com/Kong/kubernetes-ingress-controller/actions/runs/12652101132