I've done some neuro/ephys related collaborations where I installed stuff inside a room sheathed in all 6 sides in solid, grounded copper. Inside with the door shut, the wifi and LTE were both good enough to stream video!!! Although, they say it did a good job at cutting the 60hz noise. Personally I would learn a little bit more about Faraday cage design before trusting anything to it besides lightning strikes

Interesting! Do you think the signal propagated through the copper or snuck in through some hole or slit?

High-frequency emissions love long thin gaps. Just grounding the parts against each other is not enough, you have to close the longer gaps, eg with copper tape with conductive glue (sold in electronics shops) and the surface below must be blank too. If you do not do this the gaps might even function as an antenna and amplify the signal.

Also, cables coming outside of your box must be shielded too.

Typically there was a 2" conduit carrying DC power cables and the seam around the door might not have been sealed, so probably that. Also had similar results with fridges, and they have rubber seals on the door gap. So probably leaking through cracks.

If we go into questions of what a maximally malicious phone could do, rather than a question of what a normal phone actually does...

The Faraday cage would still leave the accelerometer fully functional. Now you might say "but because of drift it will rapidly diverge". Yes and no. It turns out that it's possible to detect based on "gestures" where you might be. Works better for winding irregular streets than in a gridlike street network.

If we go full Sherlock Holmes, the microphone might also overhear trains and music from stores giving away the location.

Or turn it off. Or leave it at home.