> On the Mac, I think you have to open the Music app and click on a bunch of links
Maybe there's a route like that, but at least today it's always under Apple ID management, and I find that quite logical.
On macOS it's under System Preferences -> Apple ID -> Media and Purchases -> Subscriptions: [Manage...] button. Don't have a phone at hand but it's very similar on iOS, somewhere under Settings -> Apple ID. I forgot the exact location but it's with some fairly obvious name, like "Purchases" or "Subscriptions", very hard to miss it.
Naturally, it requires learning where it is for the first time, but then it's fairly intuitive.
> In one app I clicked "start 14 day trial", but ended up being charged for an annual subscription immediately.
Hm. That's odd. Apps could be pretty deceptive and even outright scummy, but at least on iOS the system payment UI (the one where you have to double-tap the power button) was always very clear about how much and when exactly it would charge me.