Given it’s Starbucks, it’s almost certain that they will be using biofuels or have a carbon offset in place.

Given that, is there a problem with using a jet in this way?

That's a very big "given" with no evidence. ESG statements are the sort of thing that should be regarded with extreme skepticism, as are carbon offsets.

Personally, my biggest concerns are environmental impact and a waste of money that could have been used in many other ways (lower product prices, improve products, increase employee compensation etc).

I have no reason to doubt that the new CEO deserves his compensation package but we don't deserve all those emissions in our environment. And I am sure many employees deserve a few extra dollars per hour for their hard work!

I doubt that any person needs a compensation package worth tens of millions of dollars per year.

Yes there is. Offset is not a sustainable method, it just shifts the blame to someone else, and fuels aren't the only CO2 emitted by an airplane (other points are the manufacture, maintenance, logistics etc).

Also, you don't really get to choose what you fuel your private plane up with. Most places only provide plain Jet-A1. An airline has the regularity and scale to organise this themselves, a private operation surely doesn't.

And most jets aren't certified for 100% biofuel.

"Carbon offset", e.g. somebody who owns a lot of property with trees says he's totally, hypothetically, going to chop down those trees except actually he's going to sell some carbon credits instead. High likelihood he was never going to chop down the trees in the first place, or does so anyway and it's only 10 years later that anybody even notices. Oh, but there are ways to audit this they say! Auditors can look at the deforestation rates of neighboring properties to estimate the hypothetical averted deforestation caused by the sale of the carbon credits. And the guy who sold the carbon credits can pay his neighbors to chop down trees to pass this audit.

It's all a scam. A system by which rich people swap money back and forth with other rich people to absolve themselves of the climate sin they claim the rest of us are burdened with.