I have successfully cut, assembled, and started painting the trunk of my tree project. I haven’t been able to do the leaves as I don’t have my acrylic yet, but I will soon. Additionally, I have the vectors prepared for the leaves, so it will be ready to go once I have the materials.

My main question is how I should connect the leaves and stem.
Some good ways for you to connect the leaves and the stem include using slow-dry superglue, epoxy, and UV resin (allows you to apply resin and dry it whenever you want through light). Your connection method could depend on your budget and knowledge of the different attachment methods. Opinion: your tree trunk might look more “realistic” if you applied a darker stain to it, but this depends on how you would like your project to look like when finished.
For attaching acrylic to your piece I would recommend scoring the leaves at the connection points to ensure they stick together better. I do enjoy how you’ve used 2d pieces to create a 3d object, the emphasis on seperate layers adds a unique style point to your artwork.
I really like the idea, are you doing any engraving to differentiate the leaves from the rest of the tree? To put together the leaves you could engrave the outline of the last piece on the next piece to make it easier to line up when going to assemble.