TL;DW:
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You’ll want a PCIe 3.0 NVME drive at minimum for an optimal gaming experience. Anything beyond PCIe 4.0 is excessive and is a poor use of your money.
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SATA SSDs are still viable but on the cusp of unplayable.
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And lastly no one should game on a HDD/harddrive as the performance is beyond abysmal.
Yes. Texture and asset streaming is affected pretty significantly by the speed of your storage. Load times are a large part of where SSDs of different classes can help, but the better your SSD performs for I/O operations, the better for overall visual performance.