Gparted says disk is full but it isn't

Your partition /dev/sda2 shows up as "full" because it is entirely allocated to LVM, which is managing your / and /home partitions. We don't need to look directly at /dev/sda2 as a result, but rather your LVM configuration. We can see from your lsblk output:

└─sda2                      8:2    0 595.9G  0 part 
  ├─ManjaroVG-ManjaroRoot 254:0    0  29.3G  0 lvm  /
  ├─ManjaroVG-ManjaroHome 254:1    0 558.9G  0 lvm  /home
  └─ManjaroVG-ManjaroSwap 254:2    0   7.8G  0 lvm  [SWAP] 

that it is likely your entire LVM is allocated to ManjaroRoot, ManjaroHome and ManjaroSwap. This means that growing your partitions is not an option without either first adding a new LVM PV or shrinking an existing LVM LV (not a straightforward task). However, those options are treating the symptom and not the problem.

Your problem is that / on the device /dev/mapper/ManjaroVG-ManjaroRoot is full. Your /home partition is not full and is not relevant to your problem.

We can see from your du output that the largest disk usage under / are:

3.2G    /data
1.1G    /opt
7.6G    /usr
14G     /var

The usages for /data, /opt and /usr look reasonable but the outlier is /var which is using a ton of space.

Some updated information from you in chat shows this isn't a log issue as I suspected but rather a package cache issue with the pacman package cache. You can clean out old files from the cache with the command:

pacman -Sc 

You can read more about cleaning the package cache on the Arch wiki.

Your / is full. Probably a out of control /var/log, either ssh probes in messages/syslog, or mysql errors, and huge logs in /var/log/mysql.

The best course is to locate the offending files, understand what caused the errors, and delete them.

Then if the errors were understood, try to fix what caused them in the first place.