There are multiple statements in the saheehain stating that it did happen at the time and Allah :swt: knows best.
https://sunnah.com/search/?q=splitting+moon
Regarding the lack of available records elsewhere - if the ahadith are authentic and it did happen,
there are the possibilities that:
1.
Those who noticed it and paid attention were not prominent enough to pass the message on to record keepers and it died off as a rumour
2.
it was recorded by the romans and/or persian record keepers and journalists and is sitting in obscure registers somewhere.
3.
It was hidden or incinerated after narrow minded and falsely biased people who were waging war against Muslims found that it was mentioned in the Quran - just as they had certain bible verses removed or corrupted with the narrow minded, unjustly selfish, and criminal private statement "atuhadithoonahum bi ma fataha Allahu 'alaikum li yuhaajjookum 'inda Rabbikum"
Note also that many original manuscript records have been recently stolen from iraaq and from syria with witnesses stating that american soldiers were guarding people who were using forklifts to remove stacks and then setting fire to remaining scripts, with similar bombings taking place during world war two, manuscripts stolen from the library of the time of sahaabah in Yemen turning up at auctions in France and the UKofGB&NI etc, many of the manuscripts from the dead sea scrolls dissapearing after they fell into the hands of the CIA, and similar incidents.
Therefore the best basis for guidance is the Quran, and what we sincerely believe to be true from all other sources - with the Sahih Ahadeeth usually proving themselves to be more truthful than many other historical sources.
If it happened as recorded in the ahadeeth - then it is less likely that it will happen again - though Allah :swt: knows best.
If it didn't happen as recorded in the sahih ahadeeth, then it happened later or will happen in the future - this you can be certain of.
One question:
I know that seeing the sign will be beneficial if it is yet to happen, but what is the benefit of your speculative worries? Do you believe that you will gain or lose anything by pondering on the uncertainty?