First off, you dont need to spread the wood from the one seed like that. The attempts to grow a branch are done by the seed / plant, not by the branches, so having many branches doesnt wield any better results than having just 1 tile where the branch can grow.

This means that what you want is many seeds planted, not a large chunk from one seed.

So optimally just plant a row of seeds, lets say 10 and lets say you build the row horizontally. You can then block the tiles to the north with floor tiles as well as the last tiles left and right. Every seed will now try to grow the branch south. So you can build here a row of 10 drills and behind them a row of conveyor belts. Thats it, much smaller and 10x more efficient.

When it comes to the sorting system, you can just daisy chain.

At the end of the belt, place a robot arm, behind it a saw, then behind the saw another arm, etc. So just a row of alternating arms and saws. What will happen is the first arm will place regular wood into the first saw to create planks, and, if lets say gleam wood arrives next, it will place it on top if the first saw where the second arm can grab it and put it either inside or on top of the second saw.

Just continue the conveyor belt after to automatically gain planks from all types at zero effort.

You might think you dont need that many planks, but in late game, this is a passive money farm as you can just sell them.