Personally I put the PID probe in close contact with the heater. But I know many people disagree with that and prefer to tape it to the side of the FV under a bit of foam (or even better use a thermowell).
The reason I put it on the heater is that I like to make sure it doesn’t get too hot (whether or not that’s an issue for you will depend on how powerful your heater is). So I use the PID to make sure the heater itself is as an accurate temperature… then I can adjust that according to the current and target temperature of the brew - which I monitor with a separate sensor on the side of the FV (under a bit of foam).
The temperature of the brew itself should only change pretty slowly (for a 22 litre batch, anyhow) so you don’t really need a PID to look after it: just keep an eye and adjust the temp of the heater a couple of degrees up if it needs it.
From a control perspective the risk of putting the PID sensor on the side of the bucket is that there can be quite a time-delay between the controller deciding “heat is needed” and it seeing the temperature start to move… by which time the heater may have got pretty hot. Maybe that’s not a problem in practice, but as I say it’s just the way I do it: YMMV!
