FWIW it's not a gmail thing for privacy, but rather just part of the email spec. RFC 5233 talks about it.

https://www.rfc-editor.org/info/rfc5233/

It all dates back to the Andrew Messaging System at CMU, developed in the 1980's. Originally the format was "<username>+<keyword>+<args>@example.net" where the mail server would interpret the keyword and arguments to route the message in whatever unique way that keyword would dictate (e.g. bob+dist+~/mailinglist@example.net would read the file mailinglist in Bob's home directory and deliver the email to addresses listed in it). If the keyword was not recognized, it would just deliver normally. So bob@example.net and bob+alias@example.net were equivalent, and could be used to filter after the fact if desired.

Did the RFC editor get a makeover recently? It looks familiar, but also kinda… polished. Neat.