jxu10

Results 3 issues of jxu10

Since `install.sh` installs to `$PIXI_HOME/bin/pixi`, I think it's reasonable for `pixi self-update` to match the installer's logic for determining the "default pixi binary path".

### Checks - [x] I have checked that this issue has not already been reported. - [x] I have confirmed this bug exists on the [latest version](https://github.com/prefix-dev/pixi/releases) of pixi, using...

bug
pypi
configuration
lock file