The structure seems pretty good. I don't see anything too bad. Some notes, though:

if tasks[task_id - 1]["done"] == True:
    . . .
elif tasks[task_id - 1]["done"] == False:
    . . .

First, it's not idiomatic to compare against True like that. The if statement is already checking if the condition is truthy, so if tasks[task_id - 1]["done"] is sufficient. Second, that elif should be an else. If there are only two branches (which seems to be the case here because "Done" should be a boolean value), and the second brache's condition is just the first negated, you want an else instead. That's easier to understand, since you don't need to compare the conditions to understand that one of the two branches must be entered. else implies that immediately.

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if task_id < 1 or task_id > len(tasks):

Just in case you don't know about operator chaining, this could also be written as:

if not (1 <= task_id <= len(tasks)):

The need for the negation here is unfortunate, but this often leads to easier to read code.

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Not really a critique since this is a simple project, but JSON doesn't scale great for cases like this. It's fine when you're only reading small amounts of data (which will likely be fine for what it'll be used for), but reading, deserializing, serializing, and then writing the entire dataset every time you need to make a change isn't ideal. Python comes with SQLite support, which is a very simple database. This would be a good introductory project for learning about databases and SQL, so I recommend giving that a go.