It is just more probable that the Lebanese authorities suck and they forgot about this storage and its potential dangers. There is no need to go for a very complicated justification when negligence is so obvious.
Since Israel is constantly invading Lebanon's airspace and regularly bombing Lebanon itself, and since the very building which used to sit where the crater is was identified specifically as a potential target by the IDF, the 'simple explanation' is that it was blown up by the Israelis. But that doesn't make it the factually correct explanation of course, and even if it is basically correct there are still a lot of unanswered questions.
The idea that enough explosives to blow up half the capital were stockpiled at the port of the war-torn city for 6 years and the Lebanese were to stupid to figure out the danger is actually a more complex explanation and it strains credulity. Very few thinking people who are familiar with the situation in that area are giving the theory (either the 'fireworks' variant or the 'fertilizer' variant) much thought. As usual these days, the mainstream media, a few flesh-n-blood propagandists, and a ton of bots are giving the negligent accident story what legs it has.
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Edit: I retract the statement about the specific building being identified as a target. That may be inaccurate and it was more or less a conclusion I jumped to without proper geo analysis.