I ran into an issue like this, years ago. I thought my engine was about to explode or implode. With some research on this forum, either by searching tons of posts, or by asking questions (I don't recall which method), I found out that it was the u-joints of my driveshaft.

The way I confirmed it was to crawl underneath, and grab the shaft near each u-joint and give it a good shake. If you feel any movement when you shake it, then it must be that u-joint. So, I suggest you try that.

I ended up repairing that $1,500 driveshaft for about $100, including the arbor press that I needed for the job, and kept mounted to my workbench, for future use on other things. If I recall, the new u-joints cost me $50-$60, but they have Zerk grease fittings on them, and they are removable and replaceable. If they should ever wear out, which they won't, because I grease them every year or so. It was a pretty involved job, requiring surgically cutting out the u-joints, and pressing in the new ones. I have tools and am handy with them, but it wasn't an easy or simple job.

The OEM design is really crappy, as the u-joints are neither maintainable or replaceable without surgery. It is either the result of beancounters telling Toyota engineers what to do, or it is planned obsolescence.