Crank no start after engine swap?

Hollander shows they don't interchange but doesn't really show why. It does show the Matrix and Vibe interchange but only the 09-12 years, nothing earlier. I would suspect that there are either sensor or internal changes. Not uncommon for that. It also shows that the TC engine interchanges from 5/06 up to 2010 but only in the TC, not with other vehicles.
You might be able to find the changes if you go to a place like rock auto and look at the various parts like cams and sensors and see what parts are different. It could be like Chrysler with the 3.7 where they only changed 2 parts inside it that made it, so the engine didn't interchange with the others.

Hard to say because they don't say what was changed. On the 3.7 I mentioned they Changed the cam and crank tone rings, so the notches were reversed when they changed the control electronics. Swap those two parts and it works fine in the other years.
I suspect you have a similar issue. I think the block and head is the same and most of the other parts seem to be, but it only takes one part to mess things up. And because you have a GM vehicle and a Toyota, I suspect it's something to make them incompatible so that folks don't connect the two. A lot like all the other companies who want to hide the facts of who really builds what.

Here are some part numbers to look up from the 06 engine:
Crank - 134010H010
intake cam - 1350128040 Exhaust cam - 1350228010

I would probably look over the parts and see what's different. It could simply be that GM wanted 3X and 18X signals while Toyota wanted 6X and 24X. You could test that if you have access to an O-scope or rig up a test to watch how many notches are showing up from the sensors. If I remember that engine uses a bolt on reluctor wheel (# 19315-0T030) behind the crank pulley. Take a look and see if those are the same between the two. Could do the same with the cams. Might be that you just swap the crank wheel or a cam and are done.

You are welcome. I suspected that GM used their engine controls and Toyota wanted theirs. It's like other "joint ventures" where they work together to develop something but still need to change parts to make repairs harder. Glad you figured it out and got it running.