Step 5 says of set() says:

If the size of values is two or more, and one or more of the items are a CSSUnparsedValue or CSSVariableReferenceValue object, throw a TypeError.

values is a list of (CSSStyleValue or USVString). The spec only asks us to check if one of the values is a kind of CSSStyleValue object, but we also need to reject USVStrings that would represent one. This behaviour is tested in WPT and Blink/WebKit both pass it: https://wpt.fyi/results/css/css-typed-om/the-stylepropertymap/declared/set.tentative.html (Specifically the "Setting a list-valued property with a var ref() and other values throws TypeError" subtest.)

It's only in step 9 that we "create an internal representation", which includes converting strings to CSSStyleValues. Doing this earlier is one solution.

(Related, "create an internal representation" parses a string into a CSSStyleValue, but is missing the step of converting that into an internal representation.)

The same applies to append().