Assertions from Aldi: 'Tesco ran badly' (12)

I believe the answer is:

declarations

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'assertions' is the definition.
The answer and definition can be both related to communication as well as being plural nouns.
Maybe they are linked in a way I don't understand?

'aldi tesco ran badly' is the wordplay.
'badly' indicates anagramming the letters.
'aldi'+'tesco'+'ran'='alditescoran'
'alditescoran' with letters rearranged gives 'DECLARATIONS'.

'from' acts as a link.

Can you help me to learn more?

(Other definitions for declarations that I've seen before include "Official announcements" , "statements" , "Announcement" .)

I've seen this clue in The Guardian.

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