[jdk17u-dev] RFR: 8272853: improve `JavadocTester.runTests`

[Goetz Lindenmaier]

I backport this for parity with 17.0.11-oracle.

Resolved one import, probably recognized clean.

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Commit messages:
 - Backport b0028a459c7e99b5e4090cc19127f6347fe220ba

Changes: https://git.openjdk.org/jdk17u-dev/pull/2111/files
 Webrev: https://webrevs.openjdk.org/?repo=jdk17u-dev&pr=2111&range=00
  Issue: https://bugs.openjdk.org/browse/JDK-8272853
  Stats: 109 lines in 1 file changed: 97 ins; 6 del; 6 mod
  Patch: https://git.openjdk.org/jdk17u-dev/pull/2111.diff
  Fetch: git fetch https://git.openjdk.org/jdk17u-dev.git pull/2111/head:pull/2111

PR: https://git.openjdk.org/jdk17u-dev/pull/2111