it's because every device connected to a cell halves the bandwidth available to each device, and after something like 30-40 devices the cell is full.

I don't know where you're getting this from. There not how cells have worked since at least 3g, sort of sounds like how consumer grade WiFi hardware operates.

Towers are designed with sectors that are directional and each can support thousands of devices but those can't handle 10k people at a stadium.

If you had bothered to read the article youd have read they are talking about how stadiums are now using distributed antenna systems (DAS), which is basically hundreds of antennas spread over the venue and fed directly into fiber. Each one is designed to handle a small section. The carriers do need to hook into the endpoint here so this isn't something that can be setup on a whim.

I don't see it mentioned but there are also mobile units, cellular on wheels (COWS) are common one and they really easy to spot if know to look for them. Basically a cell tower on trailer that can use microwave for the back haul for when on site fiber isn't available.

If you end up at a venue and can't get service it's because the venue is too cheap to use any of these existing options. They could also be using some outdated antennas, LTE can't handle as many connections as the new 5G stuff.