S10 unrooted but still unauthorised

So it had been rooted. That probably means that the Knox "e-fuse" has been tripped, and the device is permanently flagged as having been altered. If that (Samsung) feature is what this Samsung app is checking then I'm afraid you are out of luck.

It's pretty poor of someone to sell a modified phone without indicating that it had been modified, but I suspect there is nothing you can do about that now.

How did you unroot it? If you did something other than a complete stock firmware reflash (and relocking of the bootloader, if unlocked) there's a chance that there are traces of the previous modifications still in the ROM and it's those that are being detected. If so it's possible that a reflash will solve this. But if it's the Knox flag that's the problem I'm afraid I don't know an answer.

 

What "few apps" did you download? That's not how I'd describe firmware flashing (I'd expect that to take one app and a firmware download, and I've never had it take more than a couple of minutes - though I've never reflashed a Samsung).

Knox will be mentioned in the software, but what you show doesn't indicate that the flag has been tripped. I think you boot into the bootloader to see the Knox status (Knox version merely tells you which version of Knox the phone uses: all Samsung phones have had Knox installed for many years now).

 

@Hadron is correct, flashing the original factory firmware is sound advice. Before you begin you'll need to know about Google FRP lock.

https://www.samsung.com/nz/support/mobile-devices/what-is-google-frp/

Use Frija to download the latest firmware for the device which can be flashed with Odin.


https://forum.xda-developers.com/s10-plus/how-to/tool-frija-samsung-firmware-downloader-t3910594