Yes, more years will earn more weeks of severance. The chart I believe explains this. But using your stated min number of 16 weeks for a band 4, If you have been here up to 8 years, you will walk with 16 weeks severance, if instead for example you have been here for 20 years, you will walk with 40 weeks severance. The max severance tops out at 52 weeks for everyone.
The notification day up to the termination day, you are still on the books as an employee, I recall reading they classify it as paid leave until your true termination date, on that day you are no longer an employee and that is when severance kicks in.
This is why it seems like some people can get more than 52 weeks. They are getting 52 weeks severance plus how ever many weeks during the notification period, currently at 2 months. I have noticed sometimes the notification period is 1 month, and sometimes 2, not sure how they determine that.