You know "veteran" does mean "someone with a lot of experience in something", right? In non-US countries that's even the primary meaning.

https://dictionary.cambridge.org/dictionary/english/veteran, https://www.oxfordlearnersdictionaries.com/definition/englis... both give its primary meaning as "a person who has had a lot of experience of a particular activity" or similar. Even Wikipedia gives the generic definition first, and clarifies the more specific case as "military veteran".