I don't think [Pigozhin's talk of withdrawal is a distraction] because according to
Reporting from Ukraine, both sides were already expecting a diversionary attack by the Ukrainians north of Bakhmut to threaten encircling the city.
This was published
before the Russian withdrawal from Bakhmut was announced. Therefore I don't think a withdrawal from Bakhmut (real or otherwise) would change Ukraine's strategy so there is no point in Russia pretending.
OTOH, it would make sense for Prigozhin to actually withdraw before getting encircled. He reported an increase in Ukrainian armor in this region which helped telegraph a possible diversionary attack here. As we have discussed before, the Russians are very keen to avoid getting encircled.
Blaming the withdrawal on lack of ammunition and in-fighting instead of on the threat of getting encircled could well be a face saving subterfuge right before the May 9th Victory Day celebration.