[Manual Backport 2.x] Refactor getClient and getLegacyClient to use authentication method registry (#5881)

[bandinib-amzn]

Description

Backport from d56b04 from #5881

Issues Resolved

Screenshot

Testing the changes

Check List

• All tests pass
  • yarn test:jest
  • yarn test:jest_integration
• New functionality includes testing.
• New functionality has been documented.
• Update CHANGELOG.md
• Commits are signed per the DCO using --signoff

[codecov]

Codecov Report

Attention: Patch coverage is 88.57143% with 4 lines in your changes are missing coverage. Please review.

Project coverage is 67.04%. Comparing base (2431df6) to head (42a90ba).
Report is 1 commits behind head on 2.x.

Files	Patch %	Lines
...gins/data_source/server/client/configure_client.ts	85.71%	0 Missing and 2 partials ⚠️
...ta_source/server/legacy/configure_legacy_client.ts	91.66%	0 Missing and 1 partial ⚠️
...ins/data_source/server/util/credential_provider.ts	50.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##              2.x    #5940      +/-   ##
==========================================
+ Coverage   67.03%   67.04%   +0.01%     
==========================================
  Files        3303     3305       +2     
  Lines       63626    63655      +29     
  Branches    10149    10157       +8     
==========================================
+ Hits        42653    42679      +26     
- Misses      18508    18510       +2     
- Partials     2465     2466       +1     

Flag	Coverage Δ
Linux_1	35.21% <ø> (ø)
Linux_2	55.14% <ø> (ø)
Linux_3	43.63% <88.57%> (+0.05%)	⬆️
Linux_4	35.33% <ø> (ø)
Windows_1	35.24% <ø> (ø)
Windows_2	55.10% <ø> (ø)
Windows_3	43.64% <88.57%> (+0.04%)	⬆️
Windows_4	35.33% <ø> (ø)

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[bandinib-amzn]

Failing cypress test is not related to this change.