what long term storage would be the best option for storing digital information

The biggest factor with passive storage, something that's not refreshed. Optical media that's made to last. M-DISC comes to mind, but there's no proof that worse case 100 years is a valid claim. Chemically speaking, a well kept disc should keep 100 years, but that's chemical composition in an ideal case. Nothing in manufacturing is perfect, so impurities are always going to be there robbing the lifespan of these discs.

Magnetic tape ideally lasts decades if not close to a century, but these are tapes that are kept in incredibly controlled conditions. If you've ever worked in the server world you'll know that any plain Jane LTO magnetic tape can't be trusted after collecting dust for anywhere close to five years.

We have scrolls, we have books, and we have stone tablets that have endured centuries, but the key in all of those is how well they were kept. The construction matters, but the bigger aspect is the environment they were kept in. For digital media, we don't know any real way to keep digital data in a passive state for centuries because, well, we haven't had digital data for that long. We've got really old punch cards that are close to that age, but even then, some of the oldest stacks are now sitting in hermetically sealed cases and are actively upkept to prevent UV damage by clear coating those cases on a regular basis.

And that's the thing with digital media, keeping it in an active storage rather than passive may be the key for centuries of longevity. USB sticks are fine so long as someone remembers to plug them in and allow them to refresh every some many years. Most USB sticks use ceramic capacitors, so leakage there isn't too much an issue. The bigger thing might be corrosion of the various traces and pins, but if well kept, that might take decades to eventually make an impact.

Sometimes, I like to parallel digital long term storage as the Ship of Theseus. If you keep moving the data from one device to another, it's still the same data. And in that sense, the data can live forever. Even if there's a gap of say two decades, if you can still get to the data and convert it into something modern, the data lives on. It's not the original medium, but with digital data, it doesn't have to be, that's the neat thing about digital data.

I think people still are working on trying to wrap their heads around digital data versus the way we used to do it. You know, someone might have the family bible and we've got to keep it nice and tidy and careful with it, because with analog data the medium and the information are one in the same. And I think sometimes people look at family digital photo collections like that. Like it's the family bible and that we've got to keep it safe. But if it's a USB stick that you pull out every so often, look over it, and call it day. Maybe move the photos from the Walmart USB stick that you got in 2016 to the new 800TB USB-F stick you just got from neo-Amazon in 2073, those photos can live forever. You don't have to be careful with them anymore.

I think that's one of the reasons that open formats matter so much. If you stored all your family videos in Windows Media Format, what happens when Microsoft dies in the Second US Civil War of 2038? That's not helping you in 2073 to open those files on a format you can never figure out. But say you stored it in some open format. Now all you need is an implementation of that format and a compiler. And poof, now you have a modern codec to read the files of the before times.

It's one of those fun maybe slightly existential kinds of things. Nothing lasts, no matter how hard we try, nothing will last. All things forgotten decay, we can only slow that decay down, but we can't prevent it. But things that live, things that pass through the hands of the living, those things endure because there are people who put time, one of the most precious resources we have, into them. Our reward for that investment of time is something that continues beyond the decay.

I like to think of it as the balance of the universe. You get to keep this, but only if you give a bit of time to pay for keeping it. And sometimes it's crazy to think of how much that applies to. Also I likely shouldn't reply after having a few drinks. Wooooo!!

Environment makes all the difference for passive storage, sorry I really went out there on the reply.

Laser etching in glass could probably work well for long term storage.