I don't seem to be able to find any documentation on taking snapshots of an Azure table store, and neither can I find anything on taking backups either.
I've found a few posts from a few years ago with people saying they export their table stores to another storage account via AzCopy running on a VM called by Windows scheduler, but this seems awfully archaic and would mean storing complete copies of data.
The only thing that the Azure documentation seems to mention is snapshots of blob storage and I don't think that table storage, even though it's likely to be blobs underneath, counts.
Surely there's a better way of taking regular backups of Azure table stores?
There is no table snapshot feature available (unlike blobs, which do have snapshots).
You'd need to devise your own way of making a backup of a table. Whether that is a partition-by-partition read + write, full table read plus write, or maybe some other technique (such as writing to two tables simultaneously).
Note: You still get the read-only secondary for tables (if you enable that type of storage), if you're concerned with DR.
Oh - regarding azCopy (or any other tool): Yes, those result in storing your data in another place. But snapshots could end up doing that too. While it's true that, with regular (non-premium) storage blobs, a snapshot doesn't initially take up much space (minimal, really), as the original blob changes, the snapshot grows in size to reflect the differences. And the same goes for each additional snapshot. Also, with premium storage (or managed disks, both regular and premium), snapshots take up the same amount of space as the original disk.