Can I use one upgrade card for multiple ship in my squad?

I have one stealth device upgrade card. can I apply it to both Soontir and Carnor, or do I need two cards?

and is this answer in the core rules or tourney rules?

In a tournament no, and that answer is in the tourney rules.

In a friendly, casual game, you can do whatever you and your opponent agree to allow.

Per tournament rules, you must have all the components necessary for your squad, including individual copies of ship/upgrade cards used. Proxy of cards is not permitted.

So - at a tournament, you need to have one upgrade card for each ship.

https://images-cdn.fantasyflightgames.com/filer_public/4e/1b/4e1b4113-6244-4d68-9917-586914552908/x-wing_tournamentrules_v221.pdf

For local friendly games, most people will let you do this and I have seen some print out a copy of the card to have it laid out on the table. I would always check with other players to make sure it is OK. Most people are in the same boat as far as the scarcity of certain upgrades and will let it slide, but occasionally you have somebody who is a stickler and will insist you have the actual card to use the upgrade.

People have pretty much answered the question, but I would add that it is worth checking with the store owner before using proxies in their store. This is a big deal with MTG.