I'm sorry to hear you are having trouble.
I'm not in NE, so can't advise about local doctors - but be aware that there is a serious problem with lack of GPs in many areas throughout Switzerland.
Many current practitioners are reaching retirement age, and many young doctors have little interest in going into general practice. Those that are interested are often only willing to work part time, meaning Switzerland is only training a portion of the GPs needed.
It is only going to get worse.
It is increasingly common that GPs have closed their practices to new patients. You may find that you have to travel farther afield, perhaps into a major city, to find someone willing to take you on. Just keep calling every practice within the radius of your ability to travel.
Yes, often one ends up seeing a junior doctor, sometimes there just isn't an alternative. So think how you can better utilize that appointment with a junior doctor: ask more probing questions, ask about follow-though, and if your problem is getting worse, ask if a referral to a specialist might be in order. One might need to be more proactive in a consultation with a doctor here than one is used to in the system back home.
You might find that a different insurance model - say, traditional where you don't need permission from the insurer or from a Hausarzt in order to access care - might in the long run be a better option for those in areas where it is harder to access doctors, even if the policy costs more upfront.
(But be aware that even with a traditional model, some specialists still will not see you without a referral from a GP. It's not a cost or coverage issue, rather a way of managing the patient load.)
Does your insurer offer a video medical appointment option? (Are these still allowed post-pandemic?) If so, you might look for a GP who offers video appointments, as that would give you a wider geographical range to find a provider.
I understand your frustration - but from experience, just keep plugging away, tcalling every practice within a reasonable area trying to find a doctor who can take you on. It took me several years, here's hoping you get lucky sooner than that.