install.ps1: Resolve-Java never probes the JDK it bootstrapped, so every re-run re-downloads ~180 MB

[fupelaqu]

Found reviewing PR #232 (Windows JDK bootstrap). Verified against install.ps1 as merged.

What happens

Resolve-Java (install.ps1:237-290) probes JAVA_HOME, then the PATH, and otherwise calls Install-EmbeddedJdk. It never looks at $EMBEDDED_JDK_DIR — <Target>\jdk, the JDK a previous run of the same installer may already have put there.

Both generated launchers document and implement a three-step order whose first step is exactly that directory:

REM   1. the JDK bundled into this install (present only when the installer had to
REM      bootstrap one because the host had no Java, or too old a Java)
REM   2. %JAVA_HOME%
REM   3. whatever java is on PATH

The installer implements only steps 2 and 3. It sets JAVA_HOME for the session only (deliberately, and correctly — install.ps1:282-286, a machine-wide JAVA_HOME would repoint every other tool on the box), so a later shell has no JAVA_HOME pointing at it either.

Consequence

On a host with no system Java, every re-run of the installer downloads the ~180 MB Temurin zip again and unpacks it over a perfectly good JDK. That includes the ordinary cases: upgrading the REPL version, re-running after a failed jar download, adding -NoExtensions.

Suggested fix

Probe <Target>\jdk\bin\java.exe first in Resolve-Java, through the same Get-JavaMajorFromExe check every other source gets, so a bundled JDK that already satisfies $REQUIRED_JAVA_VERSION short-circuits the bootstrap. That also makes the installer's resolution order match the one its own launchers advertise.

[fupelaqu]

Same bootstrap path: #234 (destructive delete), #236 (orphaned jdk/ on failure).