In this case, the spec allows for "commonly used" user defined values, which is unusual (how does a user defined value become commonly used enough in the first place?), measured per this site: https://taginfo.openstreetmap.org/keys/surface#values
You can find a few non English entries in there, but the vast majority and all of the most common ones are in English. "木“ has 2 entries, "wood" has >200k. I think it's pretty clear that even in cases when the specification is open, the intention is for values to be English whenever practical.
You misinterpreted the wiki page. That tag (like several others) explicitly supports user-defined values. This is useful, because you cannot define a complete set of values for something as open-ended as a way's surface. Innovations happen, and sometimes odd things are used to pave a way for a variety of reasons (art, tourist appeal, experiments, etc.)
So that table there lists all common values covering 99% of the use cases, and finally links to TagInfo for all values in use. That 'all commonly used values' bit is slightly misleading, because TagInfo lists all uncommon values, but it true in the sense that any common value missing from that table will be listed in TagInfo (being derived from the actual database).
So that table there lists all common values covering 99% of the use cases, and finally links to TagInfo for all values in use. That 'all commonly used values' bit is slightly misleading, because TagInfo lists all uncommon values, but it true in the sense that any common value missing from that table will be listed in TagInfo (being derived from the actual database).