I have completed a short campaign and I have some feedback, critique, and suggestions
This game's strongest point is it's style. It's absolutely BRIMMING with it, but I think the mechanics fall short of selling the fantasy of being a cool card wizard. The limitations of magic to capturing and summoning entire objects in a card limits the available creativity and the fantasy of being a 'wizard'. I think this is actually fairly easy to fix with some small but potent changes.
Starting Cards
The first thing we noticed felt a little weird was that character creation only gives you blank cards to start with. It seems like if you’ve been a wizard for a while, you might have a few objects or creatures already carded within reason. I gave all of my players one object card to start with, and they felt like it did a lot to flesh out their characters.
Expanded Luck Usage
My first suggestion is to expand the scope of Luck. In addition to being able to use Luck to cancel Sweat, it should be usable for Rerolls and Story Manipulation.
Rerolls: Reroll all dice and use the new result.
Change the Story: Add an element to the story to make things easier. "The mechanic left their tools outside the garage" if your players need some tools. "The crime boss left one of the windows unlocked" if the players need a way in somewhere. Very versatile.
Your 1.5 update reduced the amount of luck to make players 'less invincible', but if you give them something more to do with luck, they'll spend it on more. I implemented Luck as Reroll and plot adjustment in session 1 and my players immediately started using it for that purpose.
Expanded Summoning
My second suggestion is to expand the usability of cards. Being able to summon and unsummon things has potential, but it is limiting and falls short of feeling like 'magic'. Instead, I propose that players should be able to summon aspects of the carded thing.
For instance, if I have a Fan, instead of summoning the entire fan, I can blow a gust of wind. If I have an Armadillo, instead of summoning the armadillo, I can summon its Armor to make an ally more durable. If I have a Blood Knight, instead of summoning the entire knight, I can just summon its radical sword. Etc. This opens the door for more creative thinking, and also the creation of 'spells' that give an individual a more developed 'style'.
More Guidance
The game's mechanics are simple and robust, but I feel like they need more examples for how things might or should play out.
I come from Dungeons and Dragons, and other comparatively rules-heavy systems, so the extremely lightweight rules leave me wanting more examples for how things should work.
I decided to give each of my players one card to start with, and one of my players chose a Stop Sign that he could use as a weapon, but I wasn't sure what a stop sign would do for him. Should an attack with the stop sign do more Sweat than a fist? It's intuitive that it should work that way, but I'm a dummy that needs guidance, and I think others would benefit from it as well.
I would also personally appreciate some guidance for how you would ideally handle a turn structure if the need arose. Ultimately my biggest critique and desire is for more examples of how things might work and how to utilize the simple rules to the best effect.
In Conclusion
My little wizards were press ganged into cleaning the psychics out of a rat king's sewer lair. He threatened to eat one of them if they laid a hand on his babies (4 regular turtles). They ended up parleying with the psychics and offering to find them a new hideout, which took them through the vampire-run metro, a blasted demon wasteland, and finally to a chill fantasy district where they fought to the death with a Negotiator who was trying to reaquire the espers for the corporation that had made and lost them.
We had a lot of fun with the system, but struggled with getting our heads around the more cinematic nature of the system, and believe that these changes (especially the additional examples and guidance) would make it more fun, and a little easier for other people in our situation to make the jump.
Addendum
One of my players helped me slap together a Roll20 character sheet for Bubblegum Wizards 2, and I'd love to pass you the code if you're itnerested.