The amount of juice your entire phone needs to run for, say, a half hour can probably power just the bluetooth LE chipset for occasional wakeups for beacon-sending for... weeks? Months? (Completely made up time spans, but the BTLE chipset really does need a tiny amount of power for infrequent wakesups compared to the entire phone.) Certainly this can't last forever: if your phone is missing for long enough, the battery will eventually run down to a point where the battery controller won't let even the BTLE chipset draw any more power.
This definitely requires hardware, firmware, and software support in order to set up, which is why only Pixel 8 is supported so far. Clearly when they were designing the Pixel 8 hardware, they already knew this feature was in the pipeline, and wanted to be able to launch with a supported phone.
As far as I remember there's a separate microcontroller that controls "Find my phone" beacons without having to boot up iOS on the main application processor.
That explaines why my work iPhone has an empty battery after 2 weeks of being turned off. Good job Apple. /s
1. https://www.theverge.com/22697218/iphone-apple-ios-15-find-m... 2. https://developer.apple.com/find-my/
My RAZR MAXX could sit for months on the one charge (with already busted battery) without any cell activity.
So if you don't need the display and a hungry wireless tech to keep on constantly you can have enough juice for days, even when the phone is no longer in the power profile to have a full run.