[jdk21u-dev] RFR: 8249825: Tests sun/security/ssl/SSLSocketImpl/SetClientMode.java and NonAutoClose.java marked with @ignore

[Bara' Hasheesh]

Backport JDK-8249825 for parity with oracle.

Clean backport, enabling two tests that were previously marked as @ignore

This change includes refactoring logic to fix the existing flakiness of the tests & correctly specify which TLS should be used when running the tests.

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Commit messages:
 - Backport 86f39ab5bb58a1d1e720badd7261365398134151

Changes: https://git.openjdk.org/jdk21u-dev/pull/1921/files
  Webrev: https://webrevs.openjdk.org/?repo=jdk21u-dev&pr=1921&range=00
  Issue: https://bugs.openjdk.org/browse/JDK-8249825
  Stats: 391 lines in 2 files changed: 26 ins; 231 del; 134 mod
  Patch: https://git.openjdk.org/jdk21u-dev/pull/1921.diff
  Fetch: git fetch https://git.openjdk.org/jdk21u-dev.git pull/1921/head:pull/1921

PR: https://git.openjdk.org/jdk21u-dev/pull/1921