Ground glass stoppers (like the ones you've shown) are reasonably air-tight over the short term, for example, I might use them to hold samples for an iodine titration, over the day. You can add silicone grease to the stopper to seal it better. Now this sort of bottle is useless for shipping a substance, this is just for lab use.
Glass is generally assumed to be the most non-reactive container. There are plenty of caveats with this assumption -- lower quality of glass, strong base does attack glass, and other rare reactions. And its expensive, and heavy, and somewhat fragile.
A screw-cap stopper with a Teflon liner is good. Usually, its a soft silicone rubber liner, with a thin Teflon coating. Screwing the cap on tightly deforms the silicone for a seal, and the Teflon is non-reactive. This sort of container is required for samples that need to be shipped, unchanged, for analytical purposes. Or perhaps, to insure stability over the period of a couple of years.
You've mentioned some other requirements, and we'll get to those. But we still need a clearer view of what you applications is. You've got some herbs, and you're perhaps making isopropanol tinctures. But you seem a little obsessed with 100% airtight, sterile and non reactive containment. Why? Do you ship these? Because my solutions above are expensive. What preservatives do you add? Because without them, substances will last months or maybe a year, maybe less. If the contents won't endure that long anyway, why go so far to preserve them?
You have to think about things like that before you start making purchases.