>Are songs not just "buttons" pressed in a certain order with certain delays (and pedals and whatnot)?

The rest goes into some more delicate theory points but this is something that's easy to address. Music is not just a series of instructions that players repeat like machines. Sheet music leaves out a lot of details because it would make it unreadable to include everything and because it is expected that players will add their own interpretation. How loud or soft something is played is a good example, a composer may specifically put in some places where they feel the dynamics need to be a certain way but players can add their style elsewhere or even ignore the composer completely.

If you want to go down a rabbit hole look up The Firebird Suite Finale on youtube. There are videos of the composer, Stravinsky conducting it, along with many of others throughout the years. You could argue that Stravinsky's version is the correct version but even between different videos of him you can hear changes and I would argue they aren't even the best sounding versions.

And then of course once you get into jazz and more out there genres players start improvising. In jazz you'll often get a sheet that has a quick melody to play at the beginning and the end, with the majority of the performance expected to be improvised based on the chords given. And even those chords will often be modified by musicians because they can.