Don't the latest designs, ARMv9, make provision for battery-efficient speech-recognition models "at the edge"? If it's not here yet it will be soon.

Id reckon you can boil the model down to a very small one to extract some keywords and thatll be pretty good already. Just having the ability to hear if someone is talking would take very little battery, to consequently turn on the top-10000 word model would still be barely noticeable on these powerhouses of phones we got, I think. Haven't tested it, though.

Once a minute (or five, ten, whatever), turn on the microphone for one second. If voice detected, record a bit and process. Doesn't need to be always on, and as a feature missing keywords sometimes adds to the doubt that it exists ("I said 'pfizer' and got ads, you said 'pfizer' and didn't, must be something else).

Doesn't your phone sometimes stay on charging for some time?