Crystal or Crystal Oscillator for time sensitive device
10 seconds / year is 0.3 parts per million error (or as the time-nuts would usually put it, an error of 3 * 10^-7). A decent watch crystal is usually specified as +/- 20 ppm (2 * 10^-5), which is far worse than what you're asking for. The higher-frequency crystals used for clocking CPUs are usually worse than that.

Temperature-compensated oscillators (TCXOs) are better, in the 10^-6 range, but still worse than your spec.

Ovenized oscillators (OCXOs) can be better than 10^-7 but require watts of power, likely more than you can afford running on battery.