Yes, you pay taxes on the same income twice if you live a in state with an income tax. Typically state income taxes are low compared to the federal rate; my state is ~3% and some have none. CA is an exception with its pretty high tax rate.
Perhaps one of the reasons 40% of residents on CA have considered moving out of state in a recent survey.
Lets also not forget FICA (social security tax) that is 7.65% on the first $133K; none after that. One caviot for this tax is the employer has to match the tax paid by the employee, which raises the cost of employment and also means business owners get to pay a 15.3% FICA tax on their income. There is also no brackets on this tax; only that after $133K you no longer pay it.
This is one of the many reasons I am fiscally conservative. And before anyone asks, I would, without thought, rather keep that 15.3% myself and invest it the way I see fit.
Last, we have no national VAT (sales tax), but nearly every state and some municipalities do. PA sales tax is 6% plus an additional 2% for items purchased in Philadelphia. Philadelphia also has a high sugary beverage tax, which (low and behold) a recent study found is causing a significant rise in the amount of food shopping Philadelphians do outside the city and actually produced a net loss in tax revenue from sugary/prepared food products. Who would have thought; actually everyone. Our very liberal mayor although has doubled down on it and refused to acknowledge the study.
Jusdt to calrify a few points. The 7.65% include 6.2% for Social Security which is capped at $133K income but also 1.45% for Medicare which is not capped at all. You pay that percentage regardless of how much income you earn, even if it's $10 million. As you stated, your employer matches the 7.65% so in effect that's potential earnings you could have made but never got, a total of 15.3%.
As a retiree getting Social Security, my Medicare payments did not stop. It actually went up. My wife and I pay thousands of dollars every year for Medicare. The government takes it out of our Social Security retiree payments. So Medicare is
never "free". It's even higher for us to most as we have additional income and they charge more for Medicare as you income gets higher.
Regarding state income taxes, the reason it's legal, is because America is a Federal republic. Each state has its own government to run and services it must pay for including local police, education, building roads, public transportation,health care for its residents, parks, state militia, State Police, Fire Departments. All this is paid through State income taxes (unless the state doesn't have those taxes) plus state sales taxes, property taxes which are very high where I live in New Jersey, gasoline taxes, inheritance taxes, alcohol taxes, marijuana taxes
etc. The Federal government taxes to pay for their costs such as the military, Medicare, Social Security, health and education subsidies to the states, foreign contributions, NASA, FBI, Customs, Interior (parks and national monuments and other Federally owned property, etc. Although the government does have tariffs, there is no national sales tax like a VAT tax. Sales Taxes in the State are for the final purchaser to pay. There are no Value Added Taxes charged at previous levels of sales such as by distributors, manufacturers, etc.