Not entirely avidly, but slowly or casually (4)

I believe the answer is:

idly

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'casually' is the definition.
(I've seen this in another clue)

'not entirely avidly but' is the wordplay.
'not entirely' indicates a hidden word.
'IDLY' is hidden in the letters of 'avidly but'.

'slowly or' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for idly that I've seen before include "How one stands by?" , "Indolently" , "How one may stand by" , "In a lazy way" , "In a lazy manner" .)

I've seen this clue in the Evening Standard.

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