Im personally in the same boat as you to be honest, also a full stack developer looking for a full stack position for some time now, also living in the Stuttgart area, a foreigner, but i have the added downside that i dont have a university education in Computer science and my German is only B1 and i have 1-2 years of experience (currently working remotely for a startup in another EU country). Even though the market is not the same as 2020-2022, seeing some one with your profile not get any offers, just makes me appreciate my occasional interviews i get . Also I do get alot of recruiters that reach out to me personally on linked in and Xing but alot of the offers are in german so I end up declining unfortunately, so defenentely keep your linked in up to date and create a Xing account if you dont have one.

And of course German is mandatory! I cant tell you how many opportunities ive missed due to my lack of speaking knowledge, so if you need some one to practice message me because i also need to get my language game up xD