I need NAS device recommendations for tight-ish budget. Synology preferred for software/security.

[TribalHound]

OK, So I get that the 1st 10TB is an offsite backup of site 1 that already hosts the data somewhere on the network.
But the 2nd 10TB drive to serve as a backup for itself ? I hope you mean data already on site 2 and not a backup of the NAS on the same disc, because a backup on the same disc as the original data is just a copy, lost if that one disc fails along with the original ?

So the NAS isn't being used as a NAS but as 2 JBODs, one backing up data from site 1 and one backing up data from site 2.
In which case, there is no redundancy for a drive failure in the NAS or redundancy for drive failure at either site - only another disc that has a copy, so the data would have to be completely re-written to either the original location or the backup device if any disc fails.

In that scenario, you'd create an allocated volume (Let's call it Site 1 Backup) - from your NAS you'd set up a local business backup to save files to that volume.

However, I'd be more inclined to network a NAS at each site, that becomes your primary shared data store for that site. Using RAID1 allows access even when a disc has failed, that you can rebuilt without any down time. If space permits in your 10TB capacity - get each NAS to backup the primary data of the other.

So NAS 1 - Volume 1 - Data for Site 1 (shared access), NAS 1 - Volume 2 - backup for Site 2 (restricted access & scheduled in the evening)
NAS 2 - Volume 1 - Data for Site 2 (shared access), NAS 2 - Volume 2 - backup for Site 1 (restricted access & scheduled early morning)
You could also create multiple volumes that compartmentalise your data further.

So in effect you'd have 2 copies of your data at 1 at each different site, additionally each site is covered for a disc failure.

If you're 10TB capacity isn't enough (or in addition) use those older different sized discs as USB plug in and remove drives (locally) where you can save critical data to for each site, then pop them in a fire-proof safe or stick them in your bag and take them home. Alternatively, if 10TB is over the top, you can populate NAS 2 with them in the short term and expand capacity later.

This video by Synology gives an overview of site to site backups and replication:
https://www.youtube.com/watch?v=vlQnvIAyFg4
It may assist in targeting your systems to a clear end goal, and so avoiding having to re-set up as you expand.

Using both discs as JBOD initially you wouldn't be able to RAID it later without wiping both discs, so it's defeating the object (slightly) of getting a NAS as opposed to an external HDD enclosure plugged into any device on site and mapped as a network share.

If it helps at all, I store NO data (that I want to retain) on any PC / Tablet / Phone (if a device fails, gets damaged or stolen, I've lost nothing) - it ALL gets written / cloned to multiple DATA volumes on my main NAS (Photos / Videos / Music / Work data / Personal Data / Downloads / Software images / Cloud copies) - from which I just map a drive or use the NAS remote access tools.
My Main NAS runs a RAID1 array for that data (2 copies, but one device, same location, drive failure redundancy) - snapshots are taking daily / weekly depending on the criticality or frequency each volume changes.
Once a month I plug a USB HDD in - run a one way 'update' of my 'must not lose data' (I can always redownload software / music / movies), then unplug and it goes in the fire safe.
Since I bought a 2nd NAS (main), the old one was demoted - it runs my home surveillance and actively backs up all my primary NAS (again Raid1) to my detached garage.
When I buy a third, I'll demote the primary and then put the oldest NAS at a relative's house and use it as a critical backup device only.
The only eventuality I'm NOT covered for, is a nuclear blast big enough to take out my house, my garage, and my relative's house - at which point my data will not be critical or we'll all be dead.

Hope this helps - as for performance RAID / JBOD - no real noticeable difference from an end user perspective.