Default install will create or use 3 partitions swap root and home each partition has its own space so where is this 8 gig??
Another note is that default you get the BTRFS fikles system and a thing called snapper. Snapper takes periodic snapshots of the root files system It is recommended that you have at least 40 gig or you may run out of space. Also the normal tools does not take into account any snapshots taken so even if they say you have space you may not. If you installed to a very small partition this could be the problem
root is where packages and temp files are stored. It won’t use home. My guess is that snapper has filled the root partition even if the tools say 2 gig is free it could easily be that snapper is eating up that spae and the normal space reporting tools don’t see the space snapper uses.
If you took the default file system you have BTRFS and snapper is turned on by default. My felling is that you allocatted too little space for a system that uses snapper.
There are snapper command line tools and also a Yast module I recommend you turn off snapper and free any space it has used