Deleting files doesn't free storage on SSD

Recently my MacBook Pro (Retina, 13-inch, Early 2015) with 251 GB Flash Storage and Mac OS Catalina 10.15.7 started complaining about not enough space left on the hard disk. So I started deleting stuff. But to my surprise that didn't free up memory on the hard disk. Using the Storage Management App I saw, that for example deleting an Application reduced the storage used by Applications, but increased the storage in the category Others.

As an example see the first screenshot before deleting Microsoft Word

and the next screenshot after deleting Microsoft Word

I also looked at the issue using the terminal. Before deleting Word I saw this

❯ sudo du -m -d 1 -c
6632    ./usr
3   ./bin
1   ./sbin
4229    ./Library
0   ./com.apple.TimeMachine.localsnapshots
135562  ./System
1   ./.fseventsd
4657    ./private
0   ./.vol
89408   ./Users
11305   ./Applications
0   ./opt
1   ./dev
1713    ./Volumes
0   ./cores
253506  .
253506  total

After deleting Word I got

6632    ./usr
3   ./bin
1   ./sbin
4229    ./Library
0   ./com.apple.TimeMachine.localsnapshots
134207  ./System
1   ./.fseventsd
4663    ./private
0   ./.vol
89409   ./Users
9942    ./Applications
0   ./opt
1   ./dev
1713    ./Volumes
0   ./cores
250796  .
250796  total

It seems to me that the total of du is reduced by twice the amount, because the \Application folder got smaller, but also the \System folder got smaller, because we also have \System\Volumes\Data\Application pointing to the same directory.

I tried to follow tips on the internet like deleting localsnapshots from time machine, but I simply have none. I also tried to rebuild the spotlight index, but it also didn't help. I started in recovery mode and checked with disk util and saw the following: Snapshot is invalid

But diskutil still thinks everything is ok and didn't repair anything.

What could be causing this strange situation? And what could I do to get more free space finally? Or is my only option left deleting the whole disk and reinstalling everything again?

After you delete those files you want to be sure to empty the trash. Try that and see if the space disappears.