How can I measure the frequency of a watch crystal using my oscilloscope?

If the AVR or any MCU has a way to output the clock to an external pin, even if it divides it down, I would measure that pin. Measuring at a clock pin will interfere with the clock frequency due to capacitance of the scope probe. This way it’s buffered.

Actually I somehow doubt that the accuracy of the oscilloscope will be enough in order to adjust the frequency of the quartz crystal that to be used as a clock.

For example 1s difference in 24h is equal to 0.001% accuracy. 1s in a week is 0.00016%.

The calibration can be done with frequency meter. If you have one with 1Hz resolution, you will get 3s per 24h accuracy.

Frequency meter with 0.1Hz resolution (and properly calibrated of course) can provide 300ms per 24h accuracy.

There is an easy way (but takes longer) leave the clock to count the time for a 24h or even more and to synchronize to radio clock signals.

An alternative is to use Internet accessible time servers with the same method.

The probe will disturb the measurement, and might be why the circuit isn't oscillating. Microchip actually has an application note which explains a recommended method of confirming the frequency of the crystal oscillator. I comes with a special firmware which outputs the clock frequency (or a divided version of it depending on the chip.)

https://www.microchip.com/wwwAppNotes/AppNotes.aspx?appnote=en592059

As for your oscilloscope's precision, I would refer to any calibration documents that came with it. They should mention something about the timing precision.