I have found it quite difficult to find information about the underlying intentions behind any of the individual changes included in the 2020 Constitution. What I have found are observers speculating about the motivations after the draft for the new Constitution was submitted by the commission of experts appointed by President Abdelmadjid Tebboune ("Laraba Commission", named for the group's head, Ahmed Laraba). The International Association of Constitutional Law published an article written by Zaid Al-Ali after the commission produced the draft of the document in May 2020:
The draft proposes to make a small change to the system on decentralisation. Decentralisation in Algeria is mainly administrative. The central state maintains a very significant amount of control over decentralized institutions. The proposed changes state that specific municipalities can have their own "special system" (Article 16). It is not clear exactly what that means but at the very least it appears to open the door to asymmetry. Some commentators have expressed concern about this possibility, on the basis that it could further weaken national unity. On its own, this does not appear to be a major area of concern.
Mr. Al-Ali published the exact same block of text a few weeks later on the website for the The International Institute for Democracy and Electoral Assistance, but this time underneath the heading "Token decentralisation?".
So it seems at least that the highlighted clause could have been included as a gesture of decentralization, possibly in response to protestors which came to be known as "Hirak". I believe what Al-Ali means when he mentions "asymmetry" is that some municipalities may in fact be rewarded for submission to the central authorities with a special system while others which still protest against the government would not. Nothing I have found so far indicates that Algeria's parliament has passed or debated a law based on this clause.
Curiously, I was able to find this reddit post that links out to a now-defunct website where someone claims that you could have at one point viewed the proposed Constituion along with a file called "the minute" which was claimed to contain all of the motions made along with the corresponding votes. It was made over 2 years ago, so the timeframe fits, but the site is currently inaccessible (at least to me) which is a real bummer since I think that document would be able to either answer your question directly or at least provide a lot more insight into the internal discussions.