I’ve burned many optical media discs, but never made use of packet writing.

Its old magic. Back when CD-R media was expensive ($20 USD per disc) "closing the disc" meant never writing to the disc again. If you only put a few megabytes on the disc might mean wasting a lot of money. Instead you could "close the session" which would cost you some capacity on the disc but let you write more to it in the future. Sometimes you would want to write the same filename (but a revised file) to the disc later, but because the file was already there, you'd need to "delete" the original before writing the new version. I think this is where this packet writing mode would come into play.

Within a few years Re-writable CD-R (CDR-W) came out and most of this wasn't needed anymore. You could wipe the whole disc and start fresh.