As others mentioned that adapter needs to be installed in a M.2 Key M slot that’s usually used for NVMe SSDs.
To clarify the terms:
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SATA is an electronical interface, the protocol (“language”) it speaks is called AHCI.
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PCIe is an electronical interface (the most low-level general-purpose one in regular computers), PCIe SSDs use the protocol NVMe.
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If you see “NVMe” then you can assume that the slot or device talked about is PCIe though the language is inprecise and vague.
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The ASM 1166 HBA is good, be careful when plugging in SATA cables in since the PCB is pretty fragile and test it a bit before using the connected drives for important data: