Post cache not working on alpine runners

I'm reopening an issue because the old one was closed, but the issue still exists : https://github.com/actions/cache/issues/352

Running this action in an alpine container results in this error :

/bin/tar: unrecognized option: P
BusyBox v1.31.1 () multi-call binary.

Usage: tar c|x|t [-ZzJjahmvokO] [-f TARFILE] [-C DIR] [-T FILE] [-X FILE] [--exclude PATTERN]... [FILE]...

Create, extract, or list files from a tar file

	c	Create
	x	Extract
	t	List
	-f FILE	Name of TARFILE ('-' for stdin/out)
	-C DIR	Change to DIR before operation
	-v	Verbose
	-O	Extract to stdout
	-m	Don't restore mtime
	-o	Don't restore user:group
	-k	Don't replace existing files
	-Z	(De)compress using compress
	-z	(De)compress using gzip
	-J	(De)compress using xz
	-j	(De)compress using bzip2
	-a	(De)compress using lzma
	-h	Follow symlinks
	-T FILE	File with names to include
	-X FILE	File with glob patterns to exclude
	--exclude PATTERN	Glob pattern to exclude
[warning]Tar failed with error: The process '/bin/tar' failed with exit code 1

Start by reproducing the cache action inside an Alpine runner and inspect the tar command that fails. Done means cache save and restore work with Alpine's BusyBox tar without the reported option error.