Both are acceptable but the meaning is different. A test is a noun and has a similar meaning to an exam. A testing would be a noun that is an activity. For example, I like swimming/chocolate/jogging/football. They are all nouns. So in your sentence you have completed an activity, specifically testing. Maybe you are the examiner for a test! The exact opposite of who said your first sentence!

Here test is verb it can be used in various ways based on the tense here I completed the test is past tense so we use test ,I completed the testing means it continuing the action so we can use testing

we would only say"the testing" for testing of machinery or equipment, or for faults such as leaks in gas pipes. We would not say "finished the testing" for an examiner marking/scoring an English Exam for example.

Test is a noun (thing) and testing is a verb (action). "I just completed the test." - I just finished a specific test. I just completed the testing." - This one is not correct. It seems to be missing information. "I just completed testing (remove the), in Mr. X's class." "I just completed testing him."

The meaning is clear in both, however, you wouldn't refer to a test as 'the testing' in English, it's just not a term that's used. Like you wouldn't say 'I have to complete the testing today,' instead you would say 'I have to complete the test today.' Therefore, 'I just completed the test' is the best expression. Hope that made sense :)