Welcome!
I don’t think you need to buy a new PSU, the one you have should satisfy the power requirements of the drives.
If it were me I’d just make some new cables for the PSU to plug the drives into, that way you could make the build tidy without all the extra bunches of cables.
If you don’t’ feel comfortable making your own cables you could use sata power splitters but I think this option is less desirable because it introduces a bunch of extra connections that could be flaky and lead to data loss from intermittent power to the drives.
A middle ground between these two options is one of those Corsair 5v load balancers, while they do create extra connections, those extra connections are the more robust 6/8 pin PCIe connectors and not the finicky sata power connectors:
Edit:
Each of one of the load balancers comes with the cabling for 8 sata and 4 molex; you just need to feed it with 1 8pin CPU connector.
Just remember that it only provides 5v and 12v power, so if you tried to use it with *some NVMe drives it might have problems.