Chosen Solution
That’s a 1.8” ZIF SSD (SATA). Good luck finding a native replacement without adapters that isn’t small and overpriced :-(. The only ones that tend to be available are 64-128GB since 256GB SSDs were so expensive at the time - hardly enough for daily use. You want a 256-512GB SSD. In order to retrofit a modern drive, you’ll need to change the drive cable with one that’s designed to work with 2.5” SATA drives to start. The caddy may be a challenge to find, so I would seriously consider using low tack double sided tape and forgetting about trying to find it. Do it on the label side without the serial number. You got extremely lucky with this laptop. Most of these laptops are beyond help without hacks like 3D printed adapters to get it from uSATA to mSATA or completely hopeless in terms of fixing the issue. These laptops should be AVOIDED in the future to avoid dealing with this again unless it can be retrofitted or fixed with natively compatible parts. With laptops that can be fixed this way, it also opens your options up to use a M.2 with an adapter (M.2->SATA) if that’s all you can find. You may be able to find a close match caddy for it on eBay as well, but it may not line up 100% correctly due to the weird factory caddy.