Unless it has changed, this is the full list of things you can/cannot gift, or rather what I remember are the things you can/cannot gift since I don't pay much attention to mogstation store shit.

Cannot Gift Anymore
- Mounts
- Emotes
- Orchestrion Rolls
- Minions
- Face Paints
- Chocobo Bardings
- Fashion Accessories

Can Still Be Gifted
- Costume sets/Weapon/Armor Cosmetics [Glamours]
- Furnishings/housing items
- Fantasia
- Story skips/boosts
- Dyes

Unfortunately due to the changes, there is no way really to gift things like minions or mounts anymore unless you just flat out give real money to your friends so they can buy it themselves, and for the things that can still be gifted through the store, you can only gift them to people who are in your friends' list if I recall correctly.