Do not use the cables from the old PSU and then re-use them to the new PSU.
Only use the cables that came from your new PSU, as much as possible.
Keep your old PSU cables and new PSU Cables segregated.
The reason why is because, the PSU cables are not standardized connecting towards the PSU side. The male side of the PSU plug connecting to the female socket of the PSU itself will vary PER PSU model (So don't necessarily think a Corsair 500W PSU might be safe to use on a 600W PSU, you might get lucky but its not 100% guaranteed safe to do so). You might connect a live to a ground, and that can result to a disaster when you turn the PSU on.
https://www.gamersnexus.net/guides/2702-psa-on-mixing-modular-psu-cables-dont-do-it
And yes, you can re-use cables that didn't come from the PSU such as the SATA data cable, as they're standardized on both ends. You can buy more if you're lacking to connect additional SATA drives. Just don't mix up modular PSU cables, keep them in the PSU box that they came with or it'll be a nightmare/additional hassle figuring out which PSU plug came from what - especially if they look similar.