I c&p'd, Clav, a procedure you are familiar with, I believe.
Those are not my words, they are the instructions provided by tourbloke on his website. If you think he is making it sound overly complicated, feel free to take it up with him.
I couldn't find instructions for what to do when travelling between the UK as a non-EU country and the EU, for obvious reasons.
Tourbloke explains what to do when travelling around Europe, crossing between EU and non-EU, so yes, this is already obligatory when going to Switzerland, but will kick in for 27 new destinations.
Yes, the procedure would presumably only need to be done once at entry to and once at exit from the EU, not when crossing EU borders.
Still seems a right PITA, though I'm sure some would think it a small price to pay for their increased other rights under Brexit, whatever they perceive them to be.
Musicians themselves don't think that. The Musicians' Union here, specifically stated that returning to pre-EU rules would be undesirable.
And this site agrees:
www.helpmusicians.org.uk/news/blog/touring-after-brexit
"If in the future acts will have to pay for a carnet as US acts currently do, for example, this will be a big hassle and extra cost. Listing every single piece of equipment and merchandise you bring into a country - down to the individual plectrum by some accounts - is going to be a huge pain. Anyone who has toured in Switzerland will have an idea of what this means. You don’t want to fall foul of the authorities on this one, so we better all start doing some homework on it now. There is also the probability that artists will need to settle the tax due on all merchandise they sell, and fees they receive in the territory before they leave. We’re trying to get more info on both these things for you. For right or for wrong, for those artists who didn’t used to put all their merch sales through the books, that’s a potential 20-25% (we’re guestimating here) reduction on merch income, as well as the cost of the carnet. Add this to the falling strength of the pound, and it’s going to be a real challenge to tour."