This is really fun and innovative! I really like the idea of freely modding the gun to your heart's content, and I do see a lot of potential in this idea alone. The number of gun parts really subverts my expectations, considering this is just a one-week jam. Well done on that part!
For some criticism, I do like the idea of a longer gun is much unwieldy and should be harder to use, but I think the room sizes is just too small for quite some of the rooms, namely the dometories. Even an unupgraded gun would suffer quite a lot in that small space. It may be me being unlucky, but it seems like there were way too few gun barrels in the game. I got four variations in the end, and it effectively means most of the upgrades are not directly impacting the game in any meaningful way. I would suggest each part give some effect that is noticeable enough to force players to make a choice, like all good roguelites do. Last but not least, I think the game would be a hundred times better if there was a key to quickly toggle between tinker mode and normal mode, as pressing that small button in the top right gets old really quickly after a few rooms, not to mention a few runs.
Anyway, I think you did a great job making this game! Keep up the good work!