I know that not all states have a sales tax (for example CA, where I spent a lot of time pre-COVID, does have it) and that for someone from Europe the mix of state and local sales taxes can be quite confusing, especially the cash register shock when you find out the price on the label on the shelf isn't necessarily the price you have to pay at checkout
Yes and no. There are two kinds of warranty (note that this is about business with consumers, not business to business!):
1. Manufacturer warranty which is completely voluntary (i.e. a manufacturer can freely decide if a warranty is placed upon a product and under what conditions), although if granted then the warranty terms become legally binding (so a manufacturer can't just promise a warranty and then later decline to fulfill it if a claim is within the warranty's constraints)
2. Seller warranty which is regulated by law and mandatory (some countries use a different term than warranty, for example in Germany it's "Gewaehrleistung" while manufacturer warranty is "Garantie"). Seller warranty originates from the contract between buyer and seller and stipulates that the item has to be of merchandisable quality (requires goods to be as described, of satisfactory quality and fit for purpose) so it serves for a time that such a product can reasonably be expected to work. If a specific specimen of that product does fail prematurely then (if evidence to the contrary is absent, e.g. there are no signs of misuse of that item) there's the assumption that the failure is because the item in question was not of merchandisable quality, in which case the seller is required to either repair the item or replace it with a same or similar one at no cost to the buyer.
Like sales tax in the US, seller warranty is handled differently across EU countries. Some put a short time limitation on the assumption that a product failed because it was not of merchandisable quality (in some countries like Germany it's 6 month, after that it's up to the buyer to prove that a failure was caused because the product quality wasn't up to scratch, and the overall seller warranty coverage is capped at 2 years after the original sale), others (like the former EU member UK) work on an assumption of how long a similar item could be reasonably expected to last (so for example a washing machine which dies after 25 months would be considered to be of unsatisfactory merchandisable quality and would need to be repaired/replaced by the seller).
Seller warranty not only covers physical goods but also electronic ones (i.e. software downloads).
It should also be noted than the EU doesn't recognize implied contracts such as the US does where a sale contract between buyer and seller implies another contract between buyer and manufacturer (think shrink-wrap licenses). Unless such a constellation is explicitly stated in the contract between buyer and seller (i.e. the manufacturer becomes a contract signee and both parties are aware of this when closing the sale) then only a contract between buyer and seller exists. For this reason, shrink-wrap licenses and EULAs are generally meaningless in the EU unless they were explicitly part of the original contract (which, at least for physical goods sold through 3rd party shops, they rarely are). For the same reason, general software sales (where you buy a physical copy of some software in a 3rd party shop) in the EU have generally been not grants of a license to use but sales of goods (although with the advent of software vendor operated web stores and SaaS this has shifted somewhat). And even where an EULA becomes part of a legal contract they are limited in what they can stipulate (for example, arbitration is a no-no). Which means in the EU no EULA can prevent you from transferring your OEM Windows copy from one computer to another one, or to sell on your legally bought software.
Tl;dr: while Europeans pay more due to VAT which is higher than the sales tax in the US they also get a lot more rights and protection than US consumers. But no, seller warranty isn't "funded" by VAT, the warranty is a legal obligation put onto commercial sellers who sell to consumers.