I love the idea - I do like a niche little narrative ttrpg, and I think the angle of "post-fossil fuel community creating a museum" is a simple but interesting one! Questions to prompt the players to create their community sounds like a good way to ease players into the setting while giving them agency over the scope of the story, and the idea for playing cards seems like it could be a fun way of structuring play while also being tactile.
The art direction sounds good as well. I'll absolutely have to check out Agent of the Register as it sounds right up my alley, and the idea of using historical documents as inspiration is great. Going for a more weathered field-notes look with hand-drawn images around the text sounds cool for this idea, and sourcing images from Creative Commons seems the right move aesthetically and workload-wise. A bit random, but you might appreciate Insect Intruders, an example of a literary genre not too far from museum guide - a bestiary! Aiming to both instil a fascination with insects and help with pest control, it was made by a colonial entomologist with illustrations drawn by his wife.
As Flabbiergerm points out, fully working out and testing the system may end up being a big challenge for the scope of the jam. A peaceful narrative ttrpg is certainly more doable than something like an action ttrpg requiring dozens of classes/items/stat blocks, but the challenge will be to restrict your playing card mechanics to something you're able to quickly and concisely explain in a few pages (a tough test of discipline given all the possibilities a deck allows!). The idea of a playmat is similarly a fun and enticing one but one not strictly necessary for the jam.
Haaaaving said that, dare I suggest a new mechanic? I would love it if there was some simple optional mechanics for players to be able to draw their own simple museum map with a short descriptor of each object. I think this would fit the setting of community coming together to create the museum really well, with everyone leaning over the map as they play their cards and pass the pencil around evoking the intimacy of communal reminiscing. I loved playing Border Rising at a indie game showcase recently because of how it does this.
I'll also volunteer myself and my jam partner if you need help playtesting it further down the line 😊