[BUG]: Switch doesn't seem to work on cygwin

Version vfox version 0.5.4

OS Windows

Describe the bug

Running vfox use java@22 does not change JAVA version

$ vfox use java@22
Now using java@22.0.1+8-tem.

$ set | grep -i JAVA_HOME
JAVA_HOME='C:\Users\koppor\.version-fox\temp\1722722400-4468\java'

$ ls -la C:\Users\koppor\.version-fox\temp\1722722400-4468\java
ls: cannot access 'C:Userskoppor.version-foxtemp1722722400-4468java': No such file or directory

This java dir seems to be hard-coded:

$ vfox activate bash

export JAVA_HOME=$'C:\\Users\\koppor\\.version-fox\\temp\\1722722400-4468\\java';export __VFOX_SHELL=$'bash

Screenshots[optional]

koppor@DESKTOP-KAK953S MINGW64 /c/git-repositories/jabref (ai-pr-1)
$ vfox use java@22
Now using java@22.0.1+8-tem.

koppor@DESKTOP-KAK953S MINGW64 /c/git-repositories/jabref (ai-pr-1)
$ ./gradlew ru

> Configure project :
Project : => 'org.jabref' Java module

FAILURE: Build failed with an exception.

* What went wrong:
java.lang.UnsupportedClassVersionError: org/beryx/jlink/JlinkPlugin has been compiled by a more recent version of the Java Runtime (class file version 61.0), this version of the Java Runtime only recognizes class file versions up to 55.0
> org/beryx/jlink/JlinkPlugin has been compiled by a more recent version of the Java Runtime (class file version 61.0), this version of the Java Runtime only recognizes class file versions up to 55.0

* Try:
> Run with --stacktrace option to get the stack trace.
> Run with --info or --debug option to get more log output.
> Run with --scan to get full insights.
> Get more help at https://help.gradle.org.

BUILD FAILED in 1s
2 actionable tasks: 2 up-to-date

This refs https://github.com/version-fox/vfox/issues/305

Reproduce the failure using the vfox use java@22 and vfox activate bash entry points under Cygwin, then compare the path-handling behavior with issue 305. Trace how JAVA_HOME is exported and verify that the completed change lets Cygwin resolve the Java directory and run the requested Java version.