I figured they write it on a plant that could live thousands of years, like a tree. That way they could access the same DNA.

USB sticks, if not plugged in once in a while will eventually lose their data. The time for this is about 10 years or a bit more.

Hard drives might be a better option than a USB stick for long term storage, but they use magnets to store data and eventually they will deteriorate. With that said I have like a 20 year old hard drive that the data on it is still readable, so they can last a while. But I doubt data would be readable after a 100 years. Not impossible, depends on the quality of the drive.

But multiple generation data storage like 1000 years, you’d need to switch the data to a new drive every so often and keep plenty of backups. So the DNA method would be an interesting work around to this problem.