argument when there’s obviously a set of shared motives driving labor costs down while at the same time pushing up profit margins.

Well, just because they have shared motives doesn't mean they're going to act in concert with each other. They're competitors. One's market share loss is another's market share gain.

The fact that profit margins are up does a lot of damage to the ‘it can’t be greedflation’ theory

It might help to clarify what "it" we're talking about here, or for that matter, what exactly we're referring to with "greedflation". To be totally clear, companies will raise prices when the market will bear it, and when they have a monopoly or cartel, that can be nearly indefinitely. The thing I'm objecting to in the first place here is the notion that that's just universally the case across the entire economy, which strikes me as ridiculous and a way for the government/central bank to deflect blame for monetary inflation. And to your point - for any highly competitive market, it's a very elaborate explanation versus just that supply and demand has caused prices to increase because the supply of money has gone up, which is a very simple and fundamental phenomenon in econ. As a rule of thumb, the more diversified the market is, the less likely that is to be the case.

We did see a big supply shock when Russia partially cut out of the global energy market, causing the market to chase after oil from the remaining producers, causing an increase in price. That's not some new phenomenon, that is also just basic supply and demand. It does cause price shocks, even if their costs didn't go up, even if labor didn't see the benefit. That's not, however, some permanent state of "inflation" like monetary inflation which is just never reversed for the entire remaining lifetime of a currency - supply shocks are transient (at least until the fossil fuels actually run out).