Probably not.
You only pay state and city or county income tax if you are living or working in the state or county. In this case, "living" means your physical location and also the location of your domicile, or permanent residence. Domicile depends on facts and intent. There is no single factor that determines your domicile, it is a combination of facts and circumstances. For example, if you bought a house in Indiana in 2019, you still own the house, and you plan to return to Indiana in the future, then you are probably domiciled there, even though you have been away for several years. You don't say, but I suspect is it more likely that you are not domiciled in Indiana since 2022. But only you know that for sure. This is a reasonably good article on domicile.
https://ceritypartners.com/insights/domicile-vs-tax-residency-what-is-domicile-and-how-do-you-change...
If you are not a US citizen, green card holder or resident alien, you only pay tax on US-source income. Your research salary is not considered US-source for this purpose, because you are actually doing the work out of the country, even though the employer is inside the US.
https://www.irs.gov/individuals/international-taxpayers/source-of-income-personal-service-income
However, if you work inside the US (such as, you travel to the US one week every 6 months to meet, talk, plan new work, etc.) then 2/52nd of your salary is US and Indiana income, and you would be required to file a 1040-NR non-resident tax return for that part of your income.
In the rare case where you are a non-resident alien, and your income is not US-sourced, and not subject to US federal tax, but you are still domiciled in Indiana because you plan to return, I don't know how that would be taxed, and I would need to ask another expert.
