Self-briefed familiarisation, whether it's even lawful (no doubt some barrack room lawyer will disagree) is not a particularly sensible course of action for an instructor to take.
Well, if the subject 'plane is a certified GA type, this is not rocket science. Of course, a briefing and checkout are always a good idea, I am never against training. But a very experienced pilot, competent in light single GA 'planes, can generally check themselves out in a similar type certified GA type without problem.
Information about power settings is published in the Flight Manual, as are any operating limitations, which will also be marked. If there are any changes to the operation of the aircraft resulting from avionics installations, there will be an FMS for these. Otherwise, the use and operation of this secondary equipment should be considered optional, and will not affect the aircraft if improperly done.
Certification of the aircraft, and the equipment installation, would not allow approval, if the aircraft is very difficult to fly in any configuration. The pilot is required to be familiar with the contents of the Flight Manual, and any FMS's, but while conforming to those, and proper training, flying a new certified type of the class you are qualified in, is not overwhelming. In some cases, regulators and insurers get carried away with obsessing about pilot training.
I opine that a pilot is more likely to have a accident because they mis managed the 'plane itself, (handling or systems), rather than installed systems or the engine/propeller.
Of course more training and mentor flying will bring more wisdom, and that's always great, but good basic piloting skills are the most things to keep you safe. Hopefully you keep these fresh.
When I was a 200 or so pilot, I was asked to ferry all kinds of complex singles, and never had a problem. I'd read whatever was provided in terms of instruction in and FMS, and off I'd go. Sometimes I'd learn as I'd fly, and that's fine. It is unlikely that you will often find two similarly equipped aircraft. The mindset to understand those systems, and use them properly is the same you will need to operated a prop or retractable gear properly, read and learn, then do.