Local detached-environments created in PIXI_CACHE_DIR, not PIXI_HOME

[mwtoews]

Checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pixi, using pixi --version.

Reproducible example

Commands I ran and their output:

$ pixi self-update
✔ pixi is already up-to-date (version 0.72.0)
$ cd /tmp/
$ export PIXI_CACHE_DIR=/tmp/pixi_cache_dir
$ export PIXI_HOME=/tmp/pixi_home
$ mkdir my-project
$ cd my-project/
$ pixi init
$ pixi config set --local detached-environments true
$ cat .pixi/config.toml 
detached-environments = true
$ pixi add python
$ pixi run which python
/tmp/pixi_cache_dir/envs/my-project-10167511532199085897/envs/default/bin/python

Issue description

Docs for detached-environments say that "[t]he location of environments created for a pixi global installation can be controlled using the PIXI_HOME environment variable". It doesn't specify where local/workspace environments are specifically stored, but it's implied to be the same as local? No, it seems to be in PIXI_CACHE_DIR, as demonstrated here.

Expected behavior

Given the docs, I would have expected the detached workspace environment to be created in PIXI_HOME. But it was installed in PIXI_CACHE_DIR. Therefore, this is either a bug or room to improve and correct the docs.