Mushy peas? Value what they're not (8)

I believe the answer is:

separate

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'they're not' is the definition.
The definition suggests an adverb but the answer is not.

'mushy peas? value' is the wordplay.
'mushy' indicates an anagram (letters mushed up).
'value' becomes 'rate' (both can mean to esteem).
'peas' with letters rearranged gives 'sepa'.
'sepa'+'rate'='SEPARATE'

'what' acts as a link.

Can you help me to learn more?

(Other definitions for separate that I've seen before include "Unconnected" , "Distinct; divide" , "Pull apart" , "Distinct or discrete" , "Come apart" .)

I've seen this clue in The Guardian.

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