Since Brexit happened and everything has been firmed up, UK nationals who live in Germany require a residence permit. That process is surprisingly straightforward.
Studying in Germany is possible and requires a student visa. The same applies to vocational training. You can also apply for a permit to set up a self-employed business or incorporate a company. Researchers at universities are also welcome with an offer from a university. If you want to work in Germany and have done vocational training or have a university degree, you are good to go after applying for a job seeker’s visa. Head to Germany and find a job that allows you to apply for an employer-binding residence permit. With a job offer in your pocket, you can apply for a permit straightway. However, obtaining a residence permit in Germany is nearly impossible without vocational training or a university degree. UK degrees now need to be officially recognised in Germany.
Health insurance is required, which you get once you work or study. Speaking German to level B1 is a requirement for some permits. It goes without saying: you ought to speak German in Germany! Check out this comprehensive website for further info: https://www.make-it-in-germany.com/en/
You won’t need a visa to travel to Germany for business or a visit.