AUR (with command line tools) fail to show new version available on AUR (internet)

If you read what I sent, yes, there is like a dozen ways to get Discord, I posted a few

The simple way is to download it directly from Discord, which does not only provide a DEB package, but also a TAR file that you can decompress in your Home folder where you want. Then you can run Discord executable from there, end of story.

Also there is always some good info in the Arch Wiki Discord - ArchWiki