Microsoft's project Silica [0] may hopefully provide really long term, large capacity archive grade storage on earth. I wonder what effects interstellar radiation has on them.
Glass is pretty inert, full stop. It would depend on the voxel size but I imagine as long as you have more than a few hundered atoms per voxel/bit you will have survivability on the order of millenia, even in high radiation environments. Someone would have to do the nuclear cross section calculations to get a real bit error rate but glass is very tough stuff.
I wonder if that's actually feasible for this application.
Microdots managed about 32MiB / square centimeter (from the "you could fit the Bible 50 times in a square inch") measure. That's a completely arbitrary density to achieve, since it was photographs which were enlarged and shrunk, and you could hypothetically use any encoding for your gold etchings, and it also leaves out the question of "how fine can you etch gold plates while still having the engraving be 'robust'".
But in any case, that gives you a target area of ~325 square meters for a 100TiB archive.
That's a lot, but not like a crazy obviously impossible number like a million square km or something.
Assuming you can cut the etching down to 1m squares and stack them on top of one another that should be no problem at all. Assuming each layer is 1.2mm thick (same as a CD) that's a volume of 1m x 1m x .390m, it would fit easily in a payload fairing of any rocket that can get it into orbit.
The volume isn't a real problem, but nearly half a cubic meter of gold should also have a mass of ~7500 kilograms. You're also looking at a cost of ~$350 million, US.
(Which isn't necessarily impossible, but still a lot, especially for an interstellar probe.)
7.5 metric tons is well within the weight limit for a Falcon 9, so add about $57m for the launch costs for a total project cost of probably around $500m.
That puts it in the realm of the Voyager probes for total cost.
[0] https://www.theverge.com/2019/11/4/20942040/microsoft-projec...