Hello Declan
Peugeot do not as far as I know give specific details as to what their updates fix.
A software update may assist in altering the
emissions parameters.
I have updated Peugeot vehicles with an original
catalyst and cured some vehicles.
I have updated vehicles with aftermarket catalysts
and not had any success.

I would advise a new genuine unit along with the
update for a correct lasting repair.

HTH
Simon

PS The customer declined your correct advice!