Where do I connect C-wire to Burnham boiler?
You've got two yellow wires on the lower left.

One of those two is the C wire -- according to the wiring diagram it is the upper one, but check with a multimeter. Remember to set it to AC mode.

Once you figure that out, the easiest way to do it would be to connect it to a new terminal block.  Then connect the C wire from the thermostat to that terminal block -- this will support additional new smart thermostats as you acquire them.