Your parents don’t need every detail. They do need the truth.
STILLNESS
STILLNESS
Privacy and honesty are not in competition. You can hold plenty back and still mislead nobody, so long as the picture they have is accurate in the parts that matter. Trouble starts with the edited version that leaves out the one thing they would actually want to know. Fewer details, accurately given, works better than a full account built around an omission.
Before your next conversation, decide what they genuinely need to know and say that part clearly. Keep the rest to yourself without inventing anything to fill the space.
What have you told your parents partially to avoid lying outright?
Free, with nothing to buy inside it.