You aren't a fool. Jealousy/envy is normal. How we deal with it is what matters. You are feeling replaced a bit, and with NRE there can be a bit of that. But you also have a history with her that Karl doesn't have. That matters to most people, and she's still coming back to you. I think one of the challenges that I had to confront in order to embrace poly more fully was reminding myself of the ways in which I'm good for my partners. Polyamory allows us to meet different needs with different people. That's worth embracing! But society has taught us that it's only real love if one person can meet ALL your needs. It's bullshit. We don't do that with friends. Even if we have a 'best friend', we still have others, and it's very rare that our best friend satisfies ALL our friendship needs and desires. So, we have other friends, too...the ones we game with, the ones we workout with, or meet for lunch or invite on a trip...or whatever. We don't have to be everything to each of our partners. They stay with us because they love us, and loving ourselves is the best thing we can do to maintain that and give them the best chance of loving us.
That's the reality of polyamory in a nutshell. One person can't be all things to one other person. Even if it can seem like that during NRE, when your hormones are going wild and everything is heightened, the new person eventually becomes just another person in your life. Partner A provides the X factor, and Partner B provides the Y factor, whatever those particular attributes might be.
If Partner A (the first partner) feels left out, neglected, taken for granted, of course they should speak up. There are so many articles out there about NRE and how to handle it to avoid hurting or even losing your longer-term partner. But someone in NRE might forget to do those things. They are temporarily insane. There are things Partner A can do (as Craig Rudd suggested) and there are things the partner feeling NRE for someone else should also be doing. It's just downright rude to neglect your first partner for the new and shiny person.
In this case, I am not sure that Dawn has actually been neglecting Pip. But just the same, he is comparing himself to Karl. And Dawn is sharing TMI with Karl. He shouldn't have it thrown in his face that Karl can make her climax during intercourse, for example.
And if Pip is feeling that Karl is fitter than him, sometimes in poly our partner's other partner can inspire us to hit the gym. Yes, it's competitive, but men do tend to be competitive. And working out, getting healthier, is good for you. Pip might have been taking Dawn for granted and letting himself get into bad shape, neglect grooming, etc.
How often do we see the trope of getting that "revenge body" after being dumped by a long term partner? In this case, Pip is not being dumped, but he can work out and get in better shape anyway. That's one thing Pip can change.
I don't know if being a teetolaler is important, unless Pip is overly indulging in alcohol, which is making him less attractive socially, or helping to pack on a few unwanted pounds.
As for the 35 vacation days, I am sure all of us people from the US are entirely envious of that! But Karl and Dawn's 10 day cruise and 2 day wedding, that's 12 days, and Pip's only planning 7 days of vacation with Dawn. Maybe you should plan another 5-day trip as well, or even longer.
Pip seems to have low self esteem. Is that right, Pip? You assume Karl is better for Dawn in every way, and she'll start spending more and more time with him and eventually leave you? Was your relationship in trouble even before she and Karl started dating?