It turns out that the monthly screen recording prompts are not even the most annoying new "feature" of macOS 15 Sequoia. Behold!

"If you turn Bluetooth off you will not be able to use your Bluetooth devices." I mean, duh?!?
Does this prompt appear monthly? No, that would be far too convenient. So how often? Every. Single. Time. You. Try. To. Disable. Bluetooth.
Have I mentioned that Apple re-enables Bluetooth on every OS update on purpose? This behavior continues with macOS 15. Also, Bluetooth is notorious for security vulnerabilities; just google site:support.apple.com bluetooth "security content".
The prompt warns that I "won't be able to use a Bluetooth keyboard or mouse," despite the fact my Mac mini already has a USB keyboard and mouse plugged in. Indeed, the Mac isn't using any Bluetooth devices, and macOS knows this but doesn't care. Moreover, the Bluetooth prompt appears even when all Bluetooth-related features are disabled such as AirDrop and Handoff. There's no "intelligence" to the prompt.
Notice in the screenshot above that the Leave Bluetooth On button is blue. That indicates the button is the default, and Bluetooth will remain on when you press return, which makes the prompt passive-aggressive. Fortunately, the Turn Bluetooth Off button is focused, as indicated by the blue focus ring around it, so you can turn Bluetooth off by pressing the spacebar when the prompt is displayed, as long as you remember the distinction between return and spacebar for controls. However, that works only when the "Keyboard navigation" setting is enabled in the Keyboard pane of System Settings. I always enable that setting whenever I install macOS, but it's not enabled by default. Thus, for the majority of Mac users who don't enable the setting—and may not be aware of it—there's no focus ring in the Bluetooth prompt, and they're forced to use the mouse to click the Turn Bluetooth Off button.
At this point it would be unfair to compare macOS to Windows Vista, though. That is, it would be unfair to Vista! Under the reign of Tim Cook and Craig Federighi, macOS has actually become worse than Windows Vista, rapidly approaching the parody of Vista in Apple's old "Get a Mac" commercial. It's truly heartbreaking what they've done to a formerly great operating system.
Some updates in light of Hacker News comments:
It turns out that the Bluetooth prompt also appears on macOS 14.7! I'm not sure why I never noticed this. My Mac mini has macOS 11 through 15 installed on separate APFS volumes, and I've been testing macOS 14 Sonoma since the WWDC 2023 developer betas. I wonder if the prompt was added in a later macOS minor update?
It also turns out that the Bluetooth prompt does not appear on laptops, which have a built-in keyboard and trackpad.
A number of commenters appear to be missing the point. The issue isn't whether the existence of a warning makes sense. The issue is that the warning can't be suppressed. The prompt has no "Don't ask me again" checkbox.