I know the smell you mean.
I think I remember reading it's produced by some kind of bacteria, similar to petrichor. They'd why it's strongest in autumn and spring - the wettest seasons that also have cooler temps.
It smells similar to mountain jungle, just more fresh and less sweet, and I remember that same book saying that different wet regions have different distinctive smells because of the soil bacteria.
This was about 20 years ago, so I don't remember the title of the book at all, but maybe searching for that can help.
It could be, if it is soil bacteria, they hang out more around birch than other trees.
If this is the case though, it would probably take a couple years of planting many to get the smell near your house strongly, though I imagine using forest soil near birch would help speed up the process.
You could probably also test if this is the source by disturbing some forest soil with a shovel to see if it momentarily intensifies, maybe ๐ค