build 6x6 single post from 2x4s for swingset?
I would emphasize that it is not possible to engineer a solution to your problem without more concrete information about loads and the existing structures. But I can share some thoughts that I hope are useful.

Start with an A-frame and modify to suit your situation.
This is a common solution to the problem of handling the dynamic vertical and lateral loads of a swing set. It is also a much easier DIY project than a vertical post anchored into the ground. You could build this framing on both sides of your swing and simply attach it to the play structure. If you want a more elegant solution start with this concept in mind and adapt it to use elements of the existing structures.


Can the play structure handle it's half of the load from a swing set? Specifically, is it anchored to the ground and/or braced to handle the lateral loads? If there is no cross-bracing add an internal cross brace between the post you attach to in your diagram and the one below it. This is one half of the "A". Consider adding a second diagonal cross brace from the same post into the ground (up in your diagram). This is the other half of the "A".

On the garage side take the same approach. If you can anchor into the garage framing that's great. To keep things lined up you can anchor one or more 2x6 members against the garage so that the cross-bar attaches at a right angle. Install a diagonal brace from this point to the ground (down in your diagram). This is half of the "A". Inside the garage, especially if you already have access to the framing, install a diagonal brace to form the other half of the "A".

About making a 6x6 post from 2x6 boards and then burying it. Besides the good points raised in comments to your question I would point out that boards (2x4, 2x6, etc) are typically used for framing above ground while timbers (4x4, 6x6, etc) are routinely buried as fence posts or covered with dirt to build retaining walls. You will find pressure treated varieties of both but the boards are almost always rated for above ground exposed use only while the timbers are rated for ground contact. In the example below the top label is ground contact and the bottom is above ground only.