I have a terrible habit of finding faults with my one long-term partner whenever I'm experiencing NRE with someone new. How can I work on this?
The first step is to figure out whether this is just a weird manifestation of your NRE, or whether there really are parts of your relationship that are bothering you, and you are only able to identify them because of the context that a new relationship brings.
If it's the former - if it really is just an unconscious reaction - it can be helpful to use CBT/DBT strategies of accepting the thought without acting on it. You can reframe it as a sort of cognitive misfiring, comparable to the way that an anxiety reaction can start in the physiological and move to the psychological. Something chemical floods your system with stress signals, and your brain things "Oh no! We're stressed! Something must be terribly wrong! What is it?" - and then just grabs onto the nearest thing and makes a disastrously big deal out of something random that wouldn't feel like such a big deal in another context.
So in this case, your brain could just be misinterpreting your desire and excitement for your new partner and thinking "wow, I really want to be with Wrenvylla right now! why could that be? it must because I'm unhappy with Strenephie!" So you can look at the thought, recognize where it's coming from, and say "no, I don't think that's the best interpretation of what's going on." Just like I sometimes say "it sure feels like these dirty dishes are the end of the world, but I recognize that they really are not, and that feeling is coming from somewhere else and being projected onto the dishes." You can have the thought, take a deep breath, choose not to indulge it or act on it, and wait for it to pass.
But it might also be the case that there are things about your partner, or your relationship, that are bothering you, and you realize what's going on when you're able to see it contrasted with another partner's way of doing things. Maybe you notice "wow, it makes me really happy when Wrenvylla texts me back with a clear answer when I'm trying to plan things. I'm now realizing just how much it bothers me that Strenephie can be vague or distant over text." Or "I was braced for a fight when I had to cancel on Wrenvylla for a work thing, but she was just chill and understanding. I guess I thought it was normal to have fights over stuff like that, but now that I see how a relationship feels without this behavior, I have much less patience for it."
In that case, it's not something to try and ignore with the same accept-that-the-thought-is-there-and-move-on technique. Instead, it's okay to bring it up! Don't make it about comparison or competition - if you can, try to leave your other partners out of the discussion entirely. Just bring up what's bothering you and explain what you'd like your partner to try and change. "It's really been bothering me how it's hard to plan things with you, because when I ask if you're free on Friday, you say 'why?' or 'idk, did you plan something?' and never actually get around to committing to something or letting me know your schedule. Could we try to get in a better habit of firming up plans quickly so I can figure out what my week is like?"