And I could not find it at all on the desktop version.
Hi DaveF, currently that's not an option on the Desktop version, but it will come on a future update. Just FYI, in case you try to connect your ElectrumX server to the mobile apps, self-signed certificates aren't accepted, but you can use a certificate from any free CA like Let's Encrypt for example.
I never used their mobile version, but the mobile is much older and it looks safer. There were some problems with coinomi desktop security (about spell check in google), but not with the mobile version (which is pretty old and I like it, I use it for years)
Hi bitmover, the desktop issue you mentioned was fixed immediately, but it was concluded that no user lost funds due to it as it could not have been exploited. The user who reported it was trying to extort Coinomi, you can read the detailed forensic report here:
https://twitter.com/kimionis/status/1131945228506738688. The difference between the desktop and mobile versions are mostly features. As you said, the mobile version is much older, and features are usually implemented there first, to go into the desktop version later.