What type of sensor (w/ bluetooth)?
Chair vibrations has the potential to be hard.

A leg to floor sensor should be not too hard but you need to make it robust enough. A (gasp) microswitch and a slightly compressible pad on two legs would work. Seat surface deflection should be doable.
Light occlusion in seat area would usually work.
Piezo disc under chair leg(s) would do something. Robustness an issue.

Capacitive proximity is easy enough. Cost may be high for finished units. Doing it yourself with an IC designed for that or even a processor that has cap-sense software available could be low cost.

BLE is not the only way. An eg ESP2866 system that wakes the processor up occasionally (once a minute?) may suffice.

Ask more if desired ... .