fix: Konnect synchronizer use client from clients provider

[randmonkey]

What this PR does / why we need it:

Konnect config synchronizer uses clientProvider.KonnectClient() to fetch Konnect client. This prevents the issue happen in the scenario where initializing Konnect is slow and synchronizer did not receive the client on creating, then the synchronizer cannot get the client.

Which issue this PR fixes:

Fixes #6904
Special notes for your reviewer:

PR Readiness Checklist:

Complete these before marking the PR as ready to review:

• the CHANGELOG.md release notes have been updated to reflect any significant (and particularly user-facing) changes introduced by this PR

[team-k8s-bot]

E2E (targeted) tests with KIND-based clusters were started at https://github.com/Kong/kubernetes-ingress-controller/actions/runs/12511350747

[codecov]

Codecov Report

Attention: Patch coverage is 66.66667% with 1 line in your changes missing coverage. Please review.

Project coverage is 76.9%. Comparing base (6ca4eee) to head (0599be7).
Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
internal/manager/setup.go	0.0%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##            main   #6905     +/-   ##
=======================================
+ Coverage   76.5%   76.9%   +0.4%     
=======================================
  Files        212     214      +2     
  Lines      25246   25139    -107     
=======================================
+ Hits       19321   19342     +21     
+ Misses      4912    4780    -132     
- Partials    1013    1017      +4     

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[czeslavo]

Please hold on - #6885 will fix this issue. In #6868 I overlooked that getting the KonnectClient right away in the setup will have such consequences, but it was intended to be temporary until #6885 gets merged.

#6905 (comment)