We're not certain what it is but I tested it with the 1k resistor from 0 to 20kHz, I did not see the crossover distortion appear again at any of those frequencies. I can't comment on noise as I haven't done any real testing but just by looking at it, compares fairly well to the real TL081 I have, which is why I was so dumbfounded
Try 20kHz with enough gain for ±10V output swing and you will see other wonders of LM358.
And noise is not something you can measure on a scope unless it's really bad.
If it came from eBay, Ali or other unofficial source, assume it is counterfeit. Or salvaged. Doesn't matter what.
Salvaged can at least be useful when it comes to obsolete components, sometimes. But you better test it
In an other thread about fake OPs they did die photos, showing something similar to LM358 - probably a Chinese version. The performance was more like slightly better than expected for a real 358. Given that the OPs are not that expensive - they could as well sold the chips as what they are. There definitely would be a market for a cheap improved 358.
I'm pretty sure you can buy legit Chinese jellybeans, just not on AliBay unless you know what you are doing.
If you are bored you could order one of each sort of LM358 from LCSC (there is a dozen) and see if they are any good.
Heck, maybe you will even find this one. The topology looks more or less the same as TI version and die dimensions are similar so I presume it was originally designed as a legit LM358 rather than solely for the sake of faking TL072s and OP07s. For starters, you wouldn't bother with input swing to ground if you were doing the latter.