I need to replace the transformer for my door bell and I have some questions
on good wiring practices.

The existing (defective) transformer is attached to a metal junction box in
the middle of a cable whose primary duty seems to be providing power to the
furnace fan motor. There is also a porcelain light bulb socket (luminaire
seems too fancy a word for this fixture) attached directly to the 'broad'
face of the junction box. This house is 40 years old so who knows what's
been done around the wiring, I've had surprises before.

I expect that when I lock out the breaker and open the junction box there
will be 4 black wires on one wire nut (1 black wire coming in, 1 black wire
going out, 1 black wire for the luminaire, and 1 black wire to existing
transformer), 4 white wires on another wire nut (similar distribution as for
black wires), and 3 grounds on a third wire nut (same as before except that
the porcelain luminaire likely isn't grounded) or else attached to the metal
box.

Is this a realistic assumption for a properly designed connection?

The reason I ask is that I had a another set of assumptions for a similar
junction box that was on a switched circuit. Here the reality didn't match
my preconceived notions; instead the white wire from the bathroom ventilator
fan was attached to a sloppy-looking birds nest of ground wires; and that's
the only way it would work.

Also, is it all right to connect 4 wires with one wire nut? Information from
Ideal shows UL listed wire combinations for number/size of conductors for
each model number of Wire-Nut(R), so presumably this is okay. But is this
commonly done as good practice and relatively safe? Would it be better to
pigtail off so that I have 3 conductors under one wire nut with the pigtail
connecting the existing light and the replacement transformer with another
wire nut?

thanks!