Not sure about other states, but I believe you're thinking of muni bonds being tax-free for those who purchase them. Here's my surely incomplete, oversimplified understanding of this process:
For funding for the stadium itself, the Bears are asking for money from the Illinois Sports Facilities Authority (ISFA). The ISFA bonds out the money, which is then paid back over time using revenue from a 2% hotel tax. We are currently paying back bonds from 2003 and 2014 that were used to finance the Sox stadium with an interest rate somewhere between 5%-9% depending on the bond. The ISFA is currently paying back those bonds, so the Bears plan calls for the refinancing of those bonds, which is where some of that discrepancy is coming from (the Bears didn't include that refinance in their numbers). This is also where the Johnson statement of "no new taxes" for this proposal is coming from. TECHNICALLY, the Bears aren't asking for any new taxes, they merely want to totally monopolize that 2% hotel tax for themselves for a long time. This has caused the Sox and Chicago Red Stars to be upset at the proposal, because the Bears proposal basically takes any other team wanting to use the ISFA money out of the game for decades.
For the funding for the infrastructure improvements, the Bears are much more vague, but it's pretty clear that they'd be asking for most of this money from the state. In 2019, the state passed a capital bill that created a dedicated fund for capital improvements in the state by raising the gas tax. Similarly to ISFA, the state basically sells bonds for various capital projects and uses the revenue from the gas tax to pay those bonds back over time. Like the ISFA, no new taxes are being used to pay for this, it merely takes away hundreds of millions of dollars that could be used for other capital projects to go towards this project. Capital money generally goes towards units of government (municipalities and school districts in particular) for things that must be fixed (I've seen capital money go to schools to fix roofs that would otherwise collapse, for example), so the money going to Bears that would otherwise go to these critical infrastructure repairs would need to be paid for primarily by property taxpayers, so I would argue that the Bears proposal will inevitably raise property taxes.
So the Bears plan essentially calls for the state to bond out billions of dollars for this project. They, however, didn't put out numbers taking into account the fact that these bonds would have interest, which is why the ISFA's numbers are almost double what the Bears are saying the project would cost. Just a total non-start of a proposal from the Bears.
