Thank you for reaching out to our platform again with your question.
Are you in Germany right now with a tourist visa?
Please have a look at the following website for more information on residence permits for the purpose of employment: https://service.berlin.de/dienstleistung/305304/en/
You can find a detailed explanation of the documents required and prerequisites in order to apply for it.
Since you mentioned that you would like to stay in order to look for a job, there is a residence permit option for "qualified workers wishing to search for an employment": https://service.berlin.de/dienstleistung/324661/en/
Please note that the website states that:
"This residence permit cannot be issued to foreigners already resident in the Federal territory with another residence permit that does not entitle the holder to pursue an economic activity.
The residence permit is issued for a period of six months and does not represent an entitlement to practice an occupation. There is no possibility of extending this residence permit for the same purpose again."
In order to find out what residence permit or visa you need, have a look at this Germany Visa website: https://www.germany-visa.org/german-residence-permit/
And information by the same website on how to extend a German short-stay visa: https://www.germany-visa.org/how-to-extend-a-short-stay-german-visa/
Please have a look at all these websites, they provide all the necessary information. You can also reach out to your local Foreigners Office for more information on options to stay. Feel free to reach out to us again if you need any further information!
All the best,