That's a great question that I wish more people would ask.
ESP32s use NOR flash storage, which is usually rated for between 10,000 to 100,000 write cycles (100,000 seems to be the standard these days). Flash can't write single bytes; instead of writes a "page" of bytes, which I believe is 256 bytes. So each 256 byte page is rated for at least 100,000 cycles. When a device is rated for 100,000 cycles it's likely to be usable for at least 10 times that, but the manufacturer is not going to make any promises beyond the 100,000.
SPIFFS (and LittleFS, now used on the ESP8266 Arduino Core) perform "wear leveling", to minimize the number of times a particular page is written. So if you modify the same section of a file repeatedly, it will automatically be written to different pages of flash. FAT is not designed to work well with flash storage; I would avoid it.
Whether SPIFFS with wear leveling will be adequate for your needs depends on your needed lifetime of the device versus how much data you'll be writing and how frequently.
NVS may perform some level of wear levelling, to an extent I'm unsure about. Here, in a forum post with 2 ESP employees, they both confirm that NVS does do some form of wear levelling. NVS is best used to persist things like configuration information that doesn't change frequently. It's not a great choice for storing information that's updated often.
You mentioned that the data just needs to survive deep sleep. If that's the case, your best option (if it's large enough) is to use the ESP32's RTC static RAM. This chunk of memory will survive restarts and deep sleep mode, but will lose its state if power is interrupted. It's real RAM so you won't wear it out by writing to it frequently, and it doesn't cost a lot of energy to write to. The catch is there's only 8KB of it.
If the 8KB of RTC RAM isn't enough and you're writing too much data too frequently to trust that SPIFFS will be okay, your best bet would be an SD card. The ESP32 can talk to an SD card adapter. SD cards use NAND flash, which has a much greater lifespan than NOR and can be safely overwritten many more times (which is why these kinds of cards are usable for filesystems in devices like Raspberry Pis).
Writing to flash also takes much more energy than writing to regular RAM. If your device is going to be battery powered, the RTC RAM is also a better choice than SPIFFS or an SD card from a power savings perspective.
Finally, if you use the RTC RAM I'd recommend starting to write it over wifi before it's full, as bringing up wifi and transmitting the data could easily take long enough that you might run out of space for some samples. Using it as a ring buffer and starting the transmit process when you hit a high water mark rather than when the buffer is full would probably be your best bet.
nvs_set_blob()
with the buffer data. Each time I do this, I create a new pair key:value. More precisely, each key contains 300 bytes. – Pyonephritis