I literally ran into this myself recently replacing the SSD inside an old Chromebox.
I was literally unaware that it was an entirely different spec based on keying.
Further, it seems I can't find any reputable companies that make a SATA M.2 SSD in the 2242 size anymore. I can only find old Western Digitals that are more than double the cost of an equivalent NVMe simply because WD doesn't actually make SATA M.2s in that size anymore.
The only companies that make them in that size are all weird bogus never-heard-of-them-and-the-reviews-are-terrible.
In your case, an adapter wouldn't really be possible. The other way around maybe would have been, but adapting Sata to pcie just isn't possible. Your best bet would be to return that ssd and buy a sata m.2 one.
You COULD have gotten a 2230 which is smaller, and gotten a 3d printed filler part to fill the space. I did that with one of my laptops because the 2242 is a pain to find.
No diss. I read that slot comment above you and went, "yep, yep, yep, makes sense. Man our standards are often dumb."
Laughed with joy at your comment, because I totally get how foreign this shit is to so many people. It's like if I walked up to a building engineer asking how they know that iron beam is safe for another 50 years via their skills and I'd just be like "......do what now?"
SATA is the interface that was mostly used until a few years ago, most people are used to seeing the version using cables (with an L shaped connector at both ends, still seen on 2.5" and 3.5" hard drives) but at some point they started making SATA drives using the m.2 form factor (with a connection similar to the one pictured in the OP) but the m.2 form factor is also used by other interfaces and not all of them are physically the same (the "expansion card" looks similar, the connection can be different), m.2 NVME drives are the ones mostly seen for storage space these days so most people assume that if storage is the m.2 type of will be NVME but sometimes (especially for laptops) it will be SATA that's required instead (like in OP's case)
Picture of an m.2 storage drive can be seen here and there's a keying section that shows the difference between B and M keys: https://en.m.wikipedia.org/wiki/M.2
They said the b SATA m2 SSD key NVMe AFR actuator clusters the cache in m.2 U.2 mSATA PCIe made a SATA lata gata when she said 2.5" wasn't big enough but 3.5" was too much and LBA LP MTTR spindles the motor with 28 pins when it lost a pin while bowling for transfer rate cause you failed to defragment your USB-connected PCIe Gen 4 pokemon with AHCI finding IOPs over 9000 so the HDD Teraflopped into the EDSFF pool and RAMmed itself 6 feet under.
SATA= Slow (Max 6 Gbps)
PCIe = Fast (Max > 100 Gbps in theory)
This is the maximum rate from the drive to the motherboard. Many drives are fast enough that SATA works become the bottleneck. With PCIe, the drive can run at its full speed, whatever that may be.
Another thing to watch out for is single-sided vs double-sided. Many laptops have flush mounted m.2 slots that won't fit an SSD with chips on both sides of the board.