Same as for Norway and the Netherlands. “Extracurriculars” are simply not a thing organized by schools, and school must be 100% free for everyone (except that you are expected to provide your own basic school supplies, i.e. pencils, lined workbooks etc. School books are provided by the school untill grade 10, you must buy your own for high school).
The students are free to organize their own social events, sports practice etc. but actual sports are done through clubs and teams that have nothing to do with school. Individual teachers sometimes take it upon themselves to run vaguely academic after-school activities on school grounds - there was a classic movie club and a book club at one point, for example. There is also a choir at my school, which is typical. I believe there is also a student run bible study group - I don’t know much about them, exept they sometimes bring cookies for everyone, which is nice.
The high school I work at puts up a musical every other year - it’s financed partly through the school budget, partly from a cultural grant from the city, and is expected to make most of it back in ticket sales (usually, it does).
In all the schools I’ve worked at, it’s gone something like this:
The school budget has money to hire a director (part-time after-school staff position), and a lesser amount of money for a music director, and maybe a technical director or choreographer.
There is also a program budget (part of the school budget), which the director has control over. Rights, promotions, sets, costumes, makeup, any equipment rental, hired musicians or other staff, equipment upgrades, etc etc, all come out of this budget.
The director will also seek outside funding/in-kind donations/sponsorship in exchange for ads in the program and that sort of thing.
The money from sponsorships and ticket sales goes directly to the program, and can be saved year after year; so, a program can, if it’s managed well, develop a nice discretionary fund they can draw on to put on a particularly expensive show, invest in equipment, or whatever.
Side note - here in our area we have Kansas School for the Deaf. One problem for them is in sports they mostly play other deaf schools which means VERY long distance trips to say Colorado or Minnesota.
Now what is interesting, they have sports and specials and such but its required by law that they can NOT charge the kids nor do they have fundraisers. One woman told me the only thing she paid in all her years was her own athletic shoes for volleyball and the senior class held fundraisers in order to have a senior trip.
Just wanted to show you what a typical American school has, here is a link to a local school here in a suburb of Kansas City showing all their student clubs. As you can see they have clubs for everything from learning Chinese culture to gay/straight alliance to bible studies to robotics to making soap.