what if you lack the fragments needed to reverse engineer/reconstruct a means to access the information?

In this case the "Fragment" isnt even a fragment, it would be a completely intact start to finish monstrous amount of data.

The larger the "fragment" is, and more complete it is, the more trivial it becomes to decode it.

And since this data is being purposefully stored in a manner intended for future use, it's very likely it will be encoded in a manner to facilitate and make it as easy as possible to decode in an intuitive manner.

Id strongly suspect every individual "glass" would have some form of "clue" or "how to" at the start of it, that serves as a guide to help the consumer know they are decoding it right.

Off the top of my head one example would be encoding a bunch of digits of the Fibonacci Sequence at the start as character literals (so text form), which even in binary form when inspected physically with a microscope, any scientist would go "oh hey thats Fibonacci!"

Then after that a large blank, followed by perhaps in order the entire ANSI character set from 0 to whatever it goes to now. Or perhaps Unicode.

The whole thing is only like a megabyte or two, so it would be less than 0.1% of the storage data, but having those 2 items at the start of every disk would be an easy way for the consumer to sanity check they are "reading" the data right, and clue them into "yo there's data stored on here" very fast

what if you lack the fragments needed to reverse engineer/reconstruct a means to access the information?

Well that's a different question, because now it sounds like you're assuming that significant data loss will occur before it's read. If the storage unit itself is damaged in the meantime to where it's data is corrupted beyond recovery, then yes - that's a potential total loss scenario. Assuming however that the storage unit remains intact, I don't see how a dedicated team of smart individuals couldn't handle it, unless their technology is somehow inferior to ours.

It's also worth considering that this storage unit probably won't be their very first interactions with modern data storage systems. This may or may not be their first interaction with a data storage system that was actually written from modern times, but unless we have a total technological collapse in the intervening 10,000 years, chances are they'll have records from our time that have been copied over however many thousands of times to make it there. Afterall, to use a much less extreme example, I don't need to get my hands on a CD-Rom or Floppy Disk burned in 1991 to get a copy of Linux 0.01, it's been copied over and over through the years and is now available for download online. Data will surely degrade over time, and large chunks will get lost as people stop copying things they think are no longer important, but I feel pretty confident in the idea that enough pieces will make it that far that these scientists (techno-archeologists?) won't be starting from scratch