Li-on Button battery check and storage

I don't think so. Packaging sometimes has a hole in the plastic bubble anyway (although that may be some other battery technology).

Avoid touching them with your fingers. Button cells are liable to discharge through a fingerprint left on the insulator between the terminals, which becomes significant given their long shelf life and low capacity and very short tracking distance across the insulator. Plastic tweezers can be handy.

Cool and dry, I would expect, but I haven't researched it.

It's a date which they are expected to meet their specification. They won't suddenly die then, but expect a reduced specification, things like capacity and possibly internal resistance.

At the price I paid for a dozen recently (with similar date), I CBA to worry. :-)

The last lot are pretty much at their expiry and work perfectly well - though I doubt they will last quite as well as when they were closer to their date of manufacture.

I avoided the "cheap" Chinese suppliers but and went for Panasonic. Assuming they are genuine (Made in Indonesia) they were still cheap (1 for 4) , but it is more a matter of having them work reliably when I need them instead of having to mess around getting some in.

I too went for Panasonic:

(Bizarrely, not the same supplier as that link displays.)

I think you are right button/coin cell packaging tends to have hole in the plastic and cardboard.

I didn't find any but they have now. My multimeter prongs are almost like needles. All batteries reading 3.2v which is healthy.

(Doh - I think I've caught up)