As Andy said, if the logistics team are part of the same company/organisation then their passing on of your details is covered by legitimate business needs. Even if it's an external company then the scenario that you described would still be classed as legitimate usage of your details.
Companies who use third parties to deliver are doing it all the time, but technically they should seek authorisation to pass your details on to a delivery company working on their behalf. Most will have something buried in the small print to cover themselves, but they rarely draw your attention to it sufficiently and that is a breech of GDPR in itself.
Once you leave the company , though, it becomes a whole different kettle of rhubarb. But.... GDPR is more or less unworkable when applied to employment scenarios. Business need is a massive catch all that can be used for all sorts of legitimate and illegal activities.
Prosecutions for breech of GDPR relating to indiviuals are rare, it's mainly where a large amount of personal detail is being used in contravention of the rules that you will see prosecutions. Even then, it's amazing how many national, multi-national and governmental organisations get off so lighty.