OK I was editing my post right after your advice but it says "you have passed the time limit" and everything that I wrote was gone.
But the main thing I found is this: Swiss categorizes the inventions in 3 categories:
Service Inventions: Your company gives you a task of designing something and you create a patentable invention out of it. In Switzerland, your company has all the rights for your invention. You get nothing in extra.
Reservable Invention: Your company does not specifically asks you to design something but yet, you have created a patentable invention in a field that is in course of your company's business area. The patent rights are completely yours. If your employment contract specifically includes a clause saying "the company reserves the rights to claim on your inventions" then you need to notify your company first. If your company finds it useful and wants to claim rights on it, they are obliged to pay you (1)(2).
Other Inventions: You have created a patentable invention without any assignment from your company and it is not even in the field of activity of your employer. You have the full rights on your invention. (3)
Accordingly, the cases in Switzerland will be slightly different from Germany as follows.
Case 1.
You work for a household appliances company. You have been assigned to design a refrigerator door. You designed an innovative door that can be patented.
In Germany: You should notify your employer. If they like the idea, they should calculate a remuneration and pay you reasonably to claim rights on it. Or else (they don't like it, find it not worth patenting or sth.), you are free to patent it by yourself (exceptional cases like bad intentions or disclaiming trade secrets etc. are excluded).
In Switzerland: You should notify your employer but you will get nothing in extra.
Case 2.
You work for a household appliances company. You have been assigned to create an algorithm for the washing machine operation. You also came up with and idea for washing machine door (or refrigerator door, doesn't matter).
In Germany: You should notify your employer since the invention is still relevant with the business field of your company. Maybe your remuneration can be higher since you are not assigned to create an algorithm. Exact same procedure applies with the first case.
In Switzerland: Check your employment contract. If there is no specific clause saying that "the company may claim rights on reservable inventions" , you should notify your employer and if your employer likes your invention, they need to calculate a remuneration and pay you . If there is no such clause, too bad for the company, you have the full rights of your invention. (1)
Case 3.
You work for a household appliances company. You have assigned with designing doors. You came up with an idea of / baby diapers / escalator motors / blockchain algorithms in cryptocurrency... anything that is not the business of your company.
Neither in Germany nor in Switzerland you do not necessarily need to notify your employer. You can go and patent your idea on your own. In Germany, your employer cannot claim any rights just because they basically have given you a computer only. In Switzerland, you are protected by the Patent Act Art. 3 (3).
Case 4 (OP's Case)
You work in your company and your employer says that "you should resign your future rights". That's not legal anywhere. Even if you sign it, that does not mean a lot in a court since it's not legal.
You work in the company and your boss says "here in Switzerland company always has the patent rights". It is FALSE. You don't even need to leave your job for having the patent rights of the things that your employer does not assign you to do. It's your employer, not your owner and you are not a slave.
Case 5 (OP's Case)
You quit your job in household appliances company and started working in a competitor. You want to file a patent for an idea that is relevant with your previous employer.
In Germany, your new employer can NOT claim any rights since they have ZERO contribution to your patent. You might be (according to the national law) needed to notify your previous employer (since they can claim that they contributed the idea). Then the Case 1 conditions apply: If they claim rights on it, they have to pay you. If not, you can patent your invention by yourself.
In Switzerland, if you will be assigned in this very specific patent idea in your new company, yes, the company can have the rights and you might be end up with nothing.
Case 6 (OP's Case)
You quit your job and found a new one. You are thinking of many other beautiful ideas that you are not assigned or obliged by your company, yet the ideas are still in line with your new company's business field.
In Germany, you should first notify your current employer and if they are interested in it, they have to pay you.
In Switzerland, you are not even obliged to notify your employer unless you have a specific clause in your contract. The rights are all yours. You can go patent it if you wish.
References
(1) Benhamou, Y., Employees' Intellectual Property Rights in Switzerland, p.381
(2) Federal Act on the Amendment of the Swiss Civil Code, Art. 332
(3) Federal Act on Patents for Inventions
(4) Legal rights of employees’ inventions, Startups.ch