Bend a thin piece of sheet metal and clamp it to the housing so it barely touches the tire(s). Spin the wheels and watch the gap. If the gap stays constant, the tires are true, if not they may need to be trued OR replaced. Truing a bandsaw tire is a bit advanced, but we can cover that later.
That knocking or ticking noise when it's running is a brearing about to go bad OR one that has gone bad. If you spin the lower wheel by hand as fast as possible and still hear it, that's where the problem is and there are 2 of them. Not rocket surgery to replace them, but a bit advanced. As suggested a loose pulley may cause the same sound, but spinning by hand eliminates the pulleys as a cause.
When running in the video, the blade didn't look all that bad. As suggested it may have put a depression in the tires if left tightened for an extended time. I don't think urethane takes a set like rubber, but I could be wrong.
When testing and when you go to set it back up, back the side and rear guides off so they don't touch the blade while it's spinning. The blade looked like it was tracking on the upper wheel correctly, the gullets being centered on the tire. The bottom wheel is just along for the ride and has no say in the set up, being spaced out at the factory, and is non-adjustable. A blade that is not welded perfectly may cause the appearance of fluttering in and out. There is no cure for that except a new blade. Yours look OK in the video, but that is also easy to check by watching the gap in the table insert.
I must commend you on your first post here with a good description, good photos and the videos. Great job!
This You Tube is about a Powermatic 143 model:
This one is also very good: