As cool as it may seem I really don't think a system that requires you to know how every other job works and their best stats in order to optimize your own is a good one, from a game design perspective. Don't need healing cards, there are spells for that.

As for utility, it's situational and you really want those abilities to be reliable rather than random card draws, especially if they're going to result in feels-bad moments. Stacking half the deck defeats the purpose of the deck, but the foresight idea... that almost sounds perfect. Astrologians are supposed to be able to read fates and such, no?

What if: There are 2 cards to buff melee and tanks, 2 cards to buff ranged and heals, and 2 different utility cards + you can always see what your next card will be + you can either consume your current card to buff the next or remove it from the deck to save for later? Sleeve Draw could either give one card in each slot (may mess up your plans) or give a missing symbol like now or maybe let you choose between 3 cards though the interfacing for that sounds icky. It could also buff Redraw to only draw new cards for a limited time and/or get more charges while also drawing a card maybe.

For the type of utility... increased move speed + either reduced cast time or the ability to cast while moving might be nice though all those could be potentially bad as well. What's universally good, is not a dmg buff, and has nothing to do with healing? Hell if I know. Maybe a simple dmg reduction or mp regen (for healers only) would be good enough.

Weird ideas for utility cards: A card that does nothing on its own but buffs your next card even more. A wildcard that has a different effect each time it's drawn ranging from killing the user to a free rez without the debuff with different chances of drawing each effect depending on its power (learning them would be a pain); likewise there could be a mechanic that randomly transforms normal cards into wildcards once in a while... meh, too random. A card that gives you a symbol you don't currently have while buffing any player melee or ranged. A card that debuffs or crowd controls an enemy. A card that just damages something, a lot. A card that lets you teleport or become immune to everything for a couple seconds. A card that makes everyone in a 100y radius dance. Idk.

And for the symbols and Divination... maybe the utility cards have their own symbol while the dps cards share the other two, Divination's dmg buff caps at 2 symbols and gains an extra non-dps effect for having the 3rd? Or there could just be 9 total cards: 3 melee buff, 3 ranged buff, 3 utility, with 3 symbols each. I do like the number of threes involved there but introducing new cards might mess with lore too much.