I (in US) registered about two years ago, took about 5 minutes to get that number, but a little bit longer to research the issue. Here is the site to register:
https://lucid.verpackungsregister.org/
I vaguely remember, that there are some additional ID numbers required during the registration pocess or some other information that I did not have, I remember simply writing in 'not available' or or leaving the field blank.
After you get the number, you are supposed to register with some of the german approved trash removal firms (recyclers) in order to estimate the amount of trash (i.e. packaging) you will be mailing to germany annually and pay the appropriate fees.
I have not done this step.
I mail a couple of orders a month to Germany, it looks to me, they don't care about small sellers. Sometimes I write in the lucid number into the customs form (there is no specific field for it, I just type the number under 'company'). Sometimes, if there is no space on the customs form, I write the number on the box. I doubt that anybody checks it.
While doing the research, one thing I remember is that it is advisable to wrap your package in plain material, with no logos, as this would suggest that the package comes from a 'corporation' and may be scrutinized more.
All of my packages went thru the customs without a glitch.
