EDIT and UPDATE are rarely needed, nor helpful.
For future readers, posts need to be standalone, without any history. These sites are not forums, but:
We build libraries of high-quality questions and answers, focused on each community's area of expertise.
Future readers are not helped by seeing all kind of history.
When people wonder about what changed, they can click the time next to "edited" to see the revision history. And early answerers can be alerted using comments after a question has changed a lot.
For example, the following:
Here's my post, about this and that.
...is much better than:
Here's my post, about something.
Edit: let me add this.
Edit 2: let me replace something with that.
Only in rare occasions, like if editing an (old) question invalidates many existing answers, a warning might need to be added to the post itself, and not be buried into comments. But: only if these are major changes and there's no other way to warn future readers. Like:
Here's my post, about this and that.
(The above has been changed after some posted their answers.) ⬅ Only if REALLY useful
Alternatively one could warn future readers about major changes by editing it into answers that are now wrong (combined with a comment towards the original author, to allow for updating/deleting it).
Of course, such major updates should not have occurred to start with. Other (less destructive) updates often don't need any notification at all, not even in comments.
So yes, please rewrite to make it look like things have always been there. Future readers will be happy to read it without the burden of any history.
If a post has already been changed a lot (or when some of its answers also refer to things like "your first edit"), then consider just leaving a comment for the original author, to explain a Q&A site is not a personal help forum, and that in future situations it might be better to post a new question rather than changing an existing one so much.