The GM column is a pain to rebuild if you don't have the tricks down. If the issue is that the wheel and upper column is flopping around, and it sounds like it is, the problem is most likely deeper than where you're looking. Literally.
Use this picture for reference:
https://www.steeringcolumnservices.com/gmtilt.php
Below the bearing housing (#46) which you've removed, the tilt housing support (#63) , which provides the pivot point and lock mechanism for the tilt column, attaches to the column with four screws (#61). When the driver frequently uses the wheel as a handle to get in and out, these screws loosen up. Removing each screw, applying loctite, and reinstalling is the key to a lasting fix. This can be done without special tools if you are creative. The trickiest part is removing the tilt pivot pins (#39). There are special pullers designed for the job although I used a small slide hammer and a machine screw for years. The other challenge is to remove the the tilt return spring(#51) and locking cap(#52). The locking cap has a small, square hole that looks like it's perfect for a 1/4" drive socket. I've always used a large Phillips screwdriver though so I could apply downward pressure to release the lock. Be warned, the spring has a bunch of pressure on it. Push down and turn counter-clockwise a bit then release the spring. It won't go flying but it's definitely got some "push."
I don't usually use instructional videos but I honestly feel this job is made easier by watching someone do it.
https://www.youtube.com/watch?v=LKR3TNcahmw