In Germany, you always hold the copyright/authorship to all works you create, but your employer may receive usage rights, potentially even exclusive usage rights. The legal basis for such implicit right transfers is §43 UrhG. But there are conditions:
- the work was created in fulfillment of your duties
- you are an employee (regardless of Angestellter or Beamter)
- the transfer of rights is necessary to achieve the purpose of the contract
- your contract doesn't discuss right assignments in any other way
These conditions can be explained by example of a journalist working for a magazine. If the journalist works as an independent contractor, §43 does not apply and there has to be an explicit license. If the journalist works as an employee, the magazine gets an implicit right to publish the works that the journalist creates for the magazine. The magazine would even get exclusive usage rights, because non-exclusive rights would be incompatible with he magazine's business.
For your situation, it matters whether you are an independent Lehrbeauftragter (in which case you retain all rights not explicitly transferred) or an university employee, e.g. a professor. Then:
- creating the video lectures is a necessary part of your duties
- consequently, the university gets some usage rights to your video lectures
- exclusive usage rights are not necessary for the purposes of a public university → you can use this material elsewhere, e.g. at a different public university
- however, commercial exploitation of these works may be at odds with the purposes of the university both in regards to §43 and your loyalty obligation as an employee in general
In any case, your contract definitely discusses rights and what your contract says overrules §43. However, contracts for public university employees are complex and include collective agreements (Tarifvertrag) and parts of Beamtenrecht, if you're not a Beamte anyway.
One technique I see occasionally is professors publishing their lecture materials under public licenses such as Creative Commons BY-SA. This is generally in line with the mission of a university and ensures the content can be used outside of the university, but means that certain fair use privileges like §60a UrhG cannot be relied on.