i'll divide business taxes into taxes on sales, taxes on costs, and taxes on profits.
taxes on sales are most easily passed on to consumers, but even there it's usually not all of the tax. let's say there's no sales tax and a widget is optimally priced at $100. then the government passes a sales tax of 6%.
if businesses now make a consumer pay $106 for a widget, sales will drop at least a little, and it may not be optimally priced. in theory, the cost of the tax should be effectively split somehow between buyer and seller. so, the business might drop the price of a widget to $98, making the consumer pay $104. in that example, "only" 2/3rds of the cost of the tax is passed on to the consumer and the business has to eat the other 1/3. the exact split varies from industry to industry, product to product, etc.
taxes on costs (increased taxes or regulations on labor, raw materials, production, etc.) may or may not be passed on to the consumer. if the market in an industry is really efficient and competitive, then yes, it can behave much like an invisible sales tax, as above. if costs went up 6% (due to a new tax on imports, say) the business would quietly raise the price from $100 to maybe $104 (not the full 6%, same reasons as above).
but these days, there are many products and industries that aren't super competitive or as tightly efficient as they might be, and there are many examples where the optimal price of a product if far removed from the actual cost. coca-cola is a notorious example. i've heard it costs them around $0.03 per can of soda (likely an exaggeration, but their costs are very low compared to the price of their product). if their costs doubled to $0.06, they're not going to double the price or even hike it by $0.03. they're just going to continue to price it based on what people will pay. they're already ignoring the costs, because it they priced it relative to cost, it would be a lot cheaper.
in those types of markets, a tax on costs wouldn't be passed on at all, it would just eat into oversized profits.
finally, taxes on profits have virtually zero effect on prices because the optimal price is the same regardless of taxes on profits. after-tax profits will be lower once a tax on profits in imposed or increased, but the optimal price won't change. if the price was optimal when there was no tax on profit, then shifting the price up or down would reduce pre-tax profit. once a tax is imposed or increased, how does reducing pre-tax profit increase after-tax profit? it can't.
the only real way windfall profits taxes can hurt consumers is more indirect, such as if a company shifts production outside the u.s. to escape taxation. then if supply is reduced and distribution costs are increased, then the price might go up. a long-time windfall profits tax may also hurt competition if new ventures in that industry are discouraged because the upward potential is limited.
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