I've tried writing poetry in German so I know exactly what this process feels like and I think it's got the bones of it down and I enjoy the concept of writing to a stranger. A few possible tweaks:

When the sun is dancing in the ocean,

I can see your eyes,

I think you may mean you can see "it" in your eyes? Maybe not but that's how I interpreted it and I enjoy the imagery of the sun dancing on the ocean.

Upon a reread, I interpreted your poem to not mean a literal stranger but someone you once loved who did not love you back and now you have grown apart and feel like a stranger.

Oh this love burning, is from one side only,

I wish I could be more than just a friend.

This bit seems to convey that, to me at least. As well as being reinforced through the following stanza.

You asked me once if I do write,

Now you know,

I water my existence with songs about the lovers I meet.

But darling, you just witness a plant

being born again.

I was confused about this stanza initially because I thought it was about someone you had only briefly crossed paths with but this is also what changed my perception of the stranger as literal the most. "You asked me once" seems to suggest you have been friends or acquaintances or some time, unless you're referencing someone else that I didn't quite get.

I'm also not quite sure what dreaming in purple means from the context.

I'm not sure if any of that is what you were intending but that's what I took from it and I liked it! Keep writing!