A tweet from the official Ryu Ga Gotoku Studio Twitter seemingly indicates that Like a Dragon: Gaiden won't see a physical release in the West.
According to the Tweet, the game will be "available for download" in November, with no mention of a physical release for the game and no ability to pre-order a physical version of the game on any Western site as of right now. This lines up with a claim last month from KamurochoBros, who claimed that there is no physical ESRB version of Like a Dragon Gaiden and the game will be digital only.
It is worth noting that Japan will be getting a boxed version, at least for the PlayStation version of the game, so there's a solid chance that even if we don't get a boxed release on launch day, we'll get one further down the line.
Like a Dragon: Gaiden will be the second Yakuza game to release this year, with Like a Dragon: Ishin releasing earlier this year. Unlike that game, however, this title is a completely new game and not a remake or remaster. Like a Dragon: Gaiden will be launched later this year in November and will be available on PlayStation 5, PlayStation 4, Xbox Series X, Xbox Series S, and PC.