I imagined every container to have tracking and identification numbers so the owners could know roughly where it is at all times; and so that various government agencies could prevent import of things not allowed in their countries.

Yes, that's correct. Every container has a unique ID, and the content of each one is declared in the shipping manifest, of which the port authority, customs, the shipping company, the agricultural service etc etc, have copies. Not knowing what was in the containers is complete bullshit, everyone know at least what was declared to be in them.

Customs checks the truthfulness of the manifest by opening a small percentage of containers at random. Most containers just go through their voyage unopened. This and their standardised size is why container shipping was such a huge efficiency revolution in international transport.

Source: I worked in the industry for 6 years.