typing.Any vs object?

Yes, there is a difference. Although in Python 3, all objects are instances of object, including object itself, only Any documents that the return value should be disregarded by the typechecker.

The Any type docstring states that object is a subclass of Any and vice-versa:

>>> import typing
>>> print(typing.Any.__doc__)
Special type indicating an unconstrained type.

    - Any object is an instance of Any.
    - Any class is a subclass of Any.
    - As a special case, Any and object are subclasses of each other.

However, a proper typechecker (one that goes beyond isinstance() checks, and which inspects how the object is actually used in the function) can readily object to object where Any is always accepted.

From the Any type documentation:

Notice that no typechecking is performed when assigning a value of type Any to a more precise type.

and

Contrast the behavior of Any with the behavior of object. Similar to Any, every type is a subtype of object. However, unlike Any, the reverse is not true: object is not a subtype of every other type.

That means when the type of a value is object, a type checker will reject almost all operations on it, and assigning it to a variable (or using it as a return value) of a more specialized type is a type error.

and from the mypy documentation section Any vs. object:

The type object is another type that can have an instance of arbitrary type as a value. Unlike Any, object is an ordinary static type (it is similar to Object in Java), and only operations valid for all types are accepted for object values.

object can be cast to a more specific type, while Any really means anything goes and a type checker disengages from any use of the object (even if you later assign such an object to a name that is typechecked).

You already painted your function into a an un-typed corner by accepting list, which comes down to being the same thing as List[Any]. The typechecker disengaged there and the return value no longer matters, but since your function accepts a list containing Any objects, the proper return value would be Any here.

To properly participate in type-checked code, you need to mark your input as List[T] (a genericly typed container) for a typechecker to then be able to care about the return value. Which in your case would be T since you are retrieving a value from the list. Create T from a TypeVar:

from typing import TypeVar, List

T = TypeVar('T')

def get_item(L: List[T], i: int) -> T:
    return L[i]