It's almost certainly PCI-e 1.x.
- If it had PCI-e 2.0 support, they'd advertise it (like they do with extra SATA2 chip on this motherboard)
- PCI-e 2.0 spec was released in 2007 and the motherboard is a 2008 model. Considering that we're just getting PCI-e 4.0 support in 2020 while it was released in 2017, I think it would be unlikely to see PCI-e 2.0 in consumer-grade hardware just one year after release.
PCI Express is backwards- and forward-compatible. Versions of motherboard and expansion card PCI-e links don't have to match. They'll use the fastest standard that both devices support (PCI-e 1.x in this case).
Each PCI-e generation is twice as fast as the previous one, so the bandwidth for a PCI-e 2.0 card will be halved in a 1.x slot. This doesn't necessarily mean that the performance will be affected, because the card may not be able to saturate a PCI-e x16 link (modern GPUs work just fine on PCI-e 3.0 x8 links).
That being said, we're talking about very old hardware here. You should be able to find decent used GPUs for cheap and after the upgrade you'll probably be bottlenecked by CPU and maybe RAM, not PCI-e.