Seems like you have more than on proj library installed. This is known as a cause of trouble. You have to choose one proj version and get rid of other dangling proj libs than you might have around.
I'm not familiar with manjaro. Use find or other similar tool to find out all libproj files, like:
find /usr/lib/ -name libproj.so'*' -print
You you find other version that were not the ones installed by your proj package version 6.3.2-1, just remove them.
What is your GDAL version and which PROJ version it depends?
Check GDAL dependency
To know which proj version GDAL depends on, we can use ldd.
ldd $(which gdalinfo)
To get just the output we want:
ldd $(which gdalinfo) | grep -E 'proj|geos'
libgeos_c.so.1 => /usr/lib/x86_64-linux-gnu/libgeos_c.so.1 (0x00007f6cae6e8000)
libproj.so.15 => /usr/local/lib/libproj.so.15 (0x00007f6caa184000)
libgeos-3.7.1.so => /usr/lib/x86_64-linux-gnu/libgeos-3.7.1.so (0x00007f6ca7d42000)
Check Postgis dependency
The same works to know the exact Postgis dependencies. Looking at the error you got, you (PostgreSQL) are using /usr/lib/postgresql/postgis-3.so.
Check this:
ldd /usr/lib/postgresql/postgis-3.so