How would you feel if I, as an applicant to your startup, tell you that I want to work with you but just for a couple of months (max. 4 months)?
The exception is if you're an expert in some specialty that's relevant and underserved on the team. In that case, the relationship becomes more of a consulting role, where you do a very specific thing very effectively and in a way that it can be smoothly handed off to long-term maintainers.
Another opportunity is direct contracting for very early stage entrepreneurs. Building the prototypes or MVP's that help them understand and articulate their ideas. Even then, four months can be pretty narrow window in the real world and there's often a bias for people who'll stick around for the next phase.
One final possibility -- and the least reliant on other people's accommodation -- would be for you to just expand the period of your cycle. Can you commit 12-18 months at a time? That's actually pretty normal in the startup world, and if you manage your finances well, it can set you up for an equally long stint of solo work.
You'll generally be looking for people who are new to the industry and are just putting a toe in. More experienced entrepreneurs often have people in their network that can already help them through this phase.
Pursue smaller contracts than your ideal and expect them to grow into the relationships/opportunities you have in mind.
If you want a full-time job to see how life at a startup compares to a more traditional work environment, four months are not enough. You'd need to stay at least a year or two because only then will you have acquired sufficient responsibility to be in a position where everyone else on your team depends on you and your output and what it means to deal with the pressure of deadlines and so on.
If compensation is not that important or your objective is to work with lots of new technology or build stuff from scratch, offer non-technical entrepreneurs to build their MVP. Depending on your experience level and feature scope you may be able to implement a prototype in four months.
However: In Germany most companies have a time of probation for 3-6 months. In this time you can leave the company whenever you want. So you could simply join the company and leave it after 4 months.