Confused by PCIE ! Is my 'budget' AlderLake 6500XT build okay?

Yes, the PCIe cards can indeed be installed in PCIe slots and vis-a-vis as the PCI interface is designed as forward and backwards-compatible However,

Apparently the cross-compatibility and quality are quite variable PCIe = gen3 seems easier than gen4, though, and for your needs it sounds

pciex1 slot Yes, it'll be perfectly compatible with gen PCIE slot Upvote

pcie 4 card in pcie 3 slot The CPU feeds those and the first slot all at PCIe There are 24 lanes on the CPU and the remaining 4 lanes go to the chipset at PCIe 4