Ideally you should expand the disk within the server.

Check with commandline "df -h" within the os how much space you actually have for these paths and expand to the minimum requirements or more.

install path : /home

/tmp, /var  There's a lot of space. Why is that?

Can you please double check the install location by running “commvault status” ?
I expect the installation to be /opt/commvault

Why /tmp and /var have so much space? That depends, not sure how to answer this without detailed server information. But it might have to do with where you installed the commvault package.
Please check commvault status for these locations:

Home Directory = 
Log Directory = 
Core Directory = 
Temp Directory =

I installed it somewhere else because there was not enough space in the /opt

Home Directory = /home/commvault/Base
Log Directory = /var/log/commvault/Log_files
Core Directory = /home/commvault
Temp Directory =/home/commvault/Base/Temp

Jpb results Directory = /home/commvault/iDataAgent/jobResults

@chris_ahn if you’d like to determine why this is reporting incorrectly, that will likely require a support case. If you’d just like to clear those messages, you can do that with some additional settings. https://documentation.commvault.com/commvault/v11/article?p=8681.htm

This first one will clear the warning for /tmp:

Name: nSYSTEMP_MIN
Category: QMachineMaint
Type: Integer
Value: 0

nGALAXY_MIN will clear the warning for the Base directory and nJOBRESULTS_MIN will clear the warning for Job Results. They all take the same Category, Type, and Value.

After configuring those, it can take up to an hour before the next space check, or you can bounce services and it will check again within a couple minutes.