The first test

$ gpaw test
...
Could not find any atomic PAW-data or pseudopotentials!

You need to set the GPAW_SETUP_PATH environment variable to point to
the directories where PAW dataset and basis files are stored.  See
https://wiki.fysik.dtu.dk/gpaw/install.html#install-paw-datasets
for details.

Let’s fix that:

$ gpaw install-data --register ~/PAWDATA
...
Selected gpaw-setups-0.9.20000.tar.gz.  Downloading...
Extracting tarball into /home/jensj/PAWDATA
Setups installed into /home/jensj/PAWDATA/gpaw-setups-0.9.20000.
Setup path registered in /home/jensj/.gpaw/rc.py.
Current GPAW setup paths in order of search priority:
   1. /home/jensj/PAWDATA/gpaw-setups-0.9.20000
Installation complete.

And now …

$ gpaw test
 ----------------------------------------------------------------------------------------------
| python-3.8.5      /tmp/venv/bin/python3                                                      |
| gpaw-21.1.0       /tmp/venv/lib/python3.8/site-packages/gpaw/                                |
| ase-3.21.1        /tmp/venv/lib/python3.8/site-packages/ase/                                 |
| numpy-1.20.3      /tmp/venv/lib/python3.8/site-packages/numpy/                               |
| scipy-1.6.3       /tmp/venv/lib/python3.8/site-packages/scipy/                               |
| libxc-4.3.4       yes                                                                        |
| _gpaw             /tmp/venv/lib/python3.8/site-packages/_gpaw.cpython-38-x86_64-linux-gnu.so |
| MPI enabled       yes                                                                        |
| OpenMP enabled    no                                                                         |
| scalapack         yes                                                                        |
| Elpa              no                                                                         |
| FFTW              yes                                                                        |
| libvdwxc          no                                                                         |
| PAW-datasets (1)  /home/jensj/PAWDATA/gpaw-setups-0.9.20000                                  |
 ----------------------------------------------------------------------------------------------
Doing a test calculation (cores: 1): ... Done

Try also gpaw --parallel=2 test.