As Patrick said in the comments, your main problem is that you define your own __init__ functions when using @dataclass. If you delete it and slightly restructure your code, it should work as expected:

from dataclasses import dataclass
from typing import List

@dataclass
class Package:
    _address: List[str]

@dataclass
class Destination:
    _start: str
    _end: str
    _distance: float

@dataclass
class DestinationContainer:
    _package: Package
    _destinations: List[Destination]

    def addPkg(self, param):
        # sure this shouldn't be "self._package.append(param)"? 
        self._package = param


# works
dc = DestinationContainer(
    Package(['some address']),
    [Destination('s', 'e', 1.0)]
)
# also works
dc.addPkg(Package(['some other address']))

There is no Array datatype, but you can specify the type of my_array to be typing.List:

from dataclasses import dataclass
from typing import List

@dataclass
class Test:
    my_array: List[ChildType]

And from Python 3.9 onwards, you can conveniently just use list:

from dataclasses import dataclass

@dataclass
class Test:
    my_array: list[ChildType]

A common and efficient approach to keeping track of all instances of a class is to store each instance in a class variable of a dict by a certain key, and use a class method to retrieve an instance by the key. In your case, use the id attribute as the key:

from typing import ClassVar
from dataclasses import dataclass

@dataclass
class Feld:
    _id_to_instance: ClassVar[dict] = {}
    id: str
    value: str

    def __post_init__(self):
        self._id_to_instance[self.id] = self

    @classmethod
    def get_instance_by_id(cls, id):
        return cls._id_to_instance[id]

so that:

for id, value in ('id1', 'value1'), ('id2', 'value2'):
    Feld(id, value)

print(Feld.get_instance_by_id('id2'))

outputs:

Feld(id='id2', value='value2')

Demo: https://ideone.com/KgQH5y