For astronomical research, it's easiest when events are dated using one calendar to correlate the observations across the whole planet. No matter which calendar specifically, it just must be uniform. For cultural research, it's more important to use a local calendar and e.g. see how the supernova was related to other culturally significant events.
Also, an article written in English is bound to use the Gregorian or Julian calendar which is familiar to the readers. An article written in Arabic, or Hebrew, or Tamil, or Malay may use the respective different calendars instead, as familiar to the readers.
Extrapolating from the only example I know, I wouldn't bet on it.
Before moving to Israel I knew that Rosh HaShanah (Hebrew New Year) is a public holiday and Gregorian New Year isn't, so I expected Hebrew calendar to be somewhat visible in everyday life or at least in official documents. Turns out, with the exception of holidays — to some surprise, including the decidedly secular Independence Day — it really isn't, everyone uses Gregorian.
Again, this a difference between astronomy and history points of view. In natural sciences, one would expect the now-universal units that originated in Western science: Julian calendar, SI units, times in UTC, etc. In historical and otherwise localized studies, I would expect a local / period-salient calendar, local units as reflected in the period's documents, etc. Converting these into exact modern dates and units is sometimes hard, and subject to a debate among historians.
Outside of the Christian world, the correlations between different calendars and the Julian calendar is quite well-known, because by the time Europeans contacted people following those calendars, they can ask "what day is today" and get the Gregorian-Julian-local calendar correspondence. If you've got a stable year count (not based on reigning kings), it's easy to work out older dates. If you have regnal year numbering, and you have enough written evidence that you can decisively determine how long each king reigns for, then you can also carry that over to a complete calendrical determination.
In cases where the calendar is no longer used, you can match up calendars by looking for records corresponding to known (largely astronomical) phenomena (eclipses are particularly helpful) and get correlates that way. This is how we match the Mesoamerican Long Count to the Julian/Gregorian calendar.
That is correct, but what would that help anyone in general (for any historic reporting)? We give dates on our agreed today's scale.. as we usually would also give other measurements like masses or lengths in our scale, unless explicitly given with other earlier units?
Even today in the news you will usually hear "an earthquake happened tonite at 2am in far away land" (and only eventually added, but then explicitly the local time).
Especially for this event I wonder, how many different calendars would you want to had mentioned to be satisfied? :)
The question is rather what are the error bars with these observations. When someone says "my car broke down last week" everyone understand that that is not a precise timestamp. On the other hand if you hear "according to the telemetry the crankshaft seized at 1696606533 unix timestamp." you know that they are talking about a very precise moment in time.
The problem comes if you take the first kind of description and convert it to a unix timestamp you imply precision where there was none found originally.
So when the wikipedia entry says "According to Songshi, the official history of the Song Dynasty (sections 56 and 461), the star seen on May 1, 1006, appeared to the south of constellation Di, between Lupus and Centaurus." Do they mean that Songshi wrote down the date according to his local convention which can be converted with a high confidence to our current date system as "May 1, 1006"? Or did they just erroneously implied more accuracy than what they have?
But at current length? I think that detail would not be necessary and even kinda distracting in term of briefness. It's not really of great importance for the event itself anyway.