What's the best way to test if a batch of batteries that I ordered will last as long as advertised?
Buy three of the batteries, discharge one with a current profile that matches your application (an LCD pocket watch with a near-constant current draw of 1µA will affect a battery differently than power drill with a 10⁻⁶ duty cycle of 1A current). This will give you a discharge curve that will tell you after how much charge drawn you can still get sufficient voltage.
Put another one in a thermal chamber for two times (e.g.,) 100 hours at the top edge of its specified temperature range, and measure voltage under load before, between and after. This will allow you to estimate self-discharge under "normal" temperature, based on the usual exponential model of self-discharge speed vs temperature.
Use the third one.
Now, you ask about cycles, and that I explicitly don't mention: That's because it's really hard to predict; expect a lot of change during the first cycles (and that will depend a lot on how you charge and how much you discharge in between, aside from temperature, which is a very significant factor in how much charging changes a battery), and less later on. How many "the first" are will depend a lot on the individual battery, the charging speed, and the discharging speed, as well as at which temperatures this all happens. I don't really think there's a known shortcut around actually doing a couple dozen to hundred cycles in a temperature-controlled chamber.
Re industrial testing: I'm not a battery expert myself; a friend of mine used to be resident physical chemist in the battery acquisition department of a large car manufacturer. He told me that buying batteries for automotive-grade reliability (and that will involve mostly how well they work after hundreds of cycles) involves intense cycle testing, chemical/spectroscopical analysis, local inspection of the would-be suppliers' factories (makes a lot of a difference to battery stability how well the manufacturing process precludes metal dust from polluting the electrolyte), and continuous long-term testing even after you agreed to buy a large number of cells over a period of time, to make sure you don't have to recall battery packs that already made it to the customer. Don't really think a "I tested it for an hour and thus know well enough how this battery will perform in the field for 1000 cycles" does exist, if that's the effort these guys have to take.
As a data point for how hard battery characterization, and optimal battery usage is: This¹ very recent (published merely two months ago) paper says that common knowledge on how to form lithium batteries in the last product step is wrong, and only after rigorous testing of a somewhat sensible range of parameters they could show that the industry has been doing it "wrong" in terms of maximizing useful cycles. And "wrong" to the tune of "up to 70% of battery life time left on table due to common knowledge being wrong".
So, we might really be in an interesting time of battery research, where the models of batteries we have aren't that great, but we do a lot with them. Not an optimal place, though, to extrapolate from limited data!
¹: Cui, Xiao, et al. "Data-driven analysis of battery formation reveals the role of electrode utilization in extending cycle life." Joule (2024)., available as HTML online