Is it better to run the OS off a USB and have the /data on a separate drive?

I’m running nextcloud on ubuntu server from a USB stick plugged into a computer. I’ve mounted a 3TB drive, and configured it as the data directory.

I’ve done this mostly as a hangup from FreeNAS, where it is recommended to have a similar arrangement. The idea is to limit the spinning drive’s use (and therefore reduce failure rate).

Does this philosophy hold water here? Or is it preferable to have the speed improvements of having the os on the hard drive along with the data?

The main concern here is speed. You haven’t said the speed of the USB stick, or whether the 3 TB drive is an SSD or spinning disk, but if you’re worried about reliability, the USB stick can easily be changed for an SSD.

Computers break, and deliberately choosing one form of storage over another is just going to prolong the time before the failure, not prevent it. USB sticks are not designed for use as an OS disk, and replacing this should probably be your top priority.

The usage of USB as a hard drive aren’t good at all in reliability. They often fail, lost files, won’t write etc…

You better always think about :
ease of use

For an OS i recommand you to use a good SSD.
For Data folder it depends on how much data you will need. If you won’t need more than 2TB you can use a good HDD 3,5 or a good SSD if you have the money. If you need more, think of raid solutions or NAS.
Don’t forget that Nextcloud isn’t a backup solution but a sync/share solution. You always need to backup in another storage : data / database / config files

I agree, USB sticks are not made for 24/7 usage (in terms of durability/reliability), similar to SDcards, nor are they fast in most cases, compared to an HDD or of course SSD.

A durable small SSD is properly best for the OS and does not bring spin up/down issues. For data storage I personally use a NAS drive (WD Red and such), which is at least made for 24/7 power (not 24/7 I/O, like database or camera recording and similar).