I guess the real answer depends on how much you want to improvise. Less improvisation, more kit.

Where I grew up, we fished a lot. You need a hook and a line. Period. These, especially hooks, are hard to improvise.

If you had or could find a pole, (e.g. a stick) great. If not, you "hand jigged". Same with bait. Catch an insect, use a rolled up piece of bread, a shiny piece of metal or foil. Somehow (oh, the horror !) we managed without a knife. No reels either; we just flipped the fish onto the ground. If you could find a piece of cork or something else that would float, you could make a bobber.

I got a lot of snappers with a stick, line, hook and some bait. Nothing fancy.

Locally (Chesapeake Bay, Maryland)there is something called "chicken necking." You tie a piece of chicken neck (or a piece chicken bone with some meat or skin left on it) to a piece of string. Throw it off the dock and let it sink. Come back in a while and pull it up. The local crabs will hang onto the chicken neck until you have to pull them off. Repeat as necessary. Result? Crabs and beer.

So, IMO, for a fishing kit, hooks and line. All else is optional, can be improvised, and just makes it simpler/easier if you don't have to improvise: easier, but not necessary.

Fishing does not need to be elaborate or equipment intensive. But, it is a lot more fun picking out and buying neat equipment.