Applying updates to legally obtained backups of games you own is permissible in many jurisdictions. Downloading NSP files from unauthorized sources for games you do not own is piracy.
– Running NSP updates generally requires custom firmware (Atmosphere, SX OS, etc.) and a means to install unsigned code. Many users have reported that version 1.4.0 runs stably on firmware 9.2.0 or higher, though newer firmware versions may require updated signature patches. Luigi-Mansion-3-NSP-Update-1---40-1--41-.4.0-Mu...
Since the filename you provided ( Luigi-Mansion-3-NSP-Update-1---40-1--41-.4.0-Mu... ) suggests a specific focus on the game update and the file format (NSP), I have drafted a blog post tailored to an audience looking for information on patch notes, installation, and file details. Applying updates to legally obtained backups of games