Your question is backwards.
First you determine what situations you are willing to deal with on the road, THEN you decide what you need to take with you to deal with them - and what know-how you may need to acquire.
Many people only want to deal with flat tires and loose bolts/screws. In that case, whatever you need to fix a flat (spare glued tire/spare tube/patch kit/(all that stuff I read about for tubeless - plugs? sealant?)) and to inflate the tire (pump or CO2) - plus maybe a tire lever or two (they're light and small enough that the penalty for carrying them is negligible). And, a basic multi-tool (hex wrenches - not forgetting the all-important 8 mm for crank arm bolts/screw heads/torx wrench/etc.). Many of us are willing to let it go at that, and if something more serious happens then limp home as best we can or call wife/Mommy/Uber for a ride.
If you want to be able to repair a broken/bent chain, then get a multi-tool with a chain breaker (and, learn to use it - on an old chain or on links left over from your last chain replacement) and a quick link (or two - those suckers get lost easily out in the wild).
If you want to repair a broken spoke, then get a multi-tool with spoke wrenches, and carry a couple of spokes - you may need more than one length - and learn how to install and tighten a spoke.
If you want to repair a broken cable, you'll need to carry spares.
And so on. I've heard of people carrying spare derailleur hangers, even. In theory, you could carry tools and spares to fix almost anything, even if you might need a trailer or panniers to schlep it all.
(Oops, forgot the most important: money and/or credit card - though many youngsters keep their payment method on their phones nowadays, or so I've heard.)