Opus 17 is assuming that you are working remotely by your own choice, not because your employer requires you to work remotely. But we have not established that. You have not provided any information one way or the other.
Employers are usually reluctant to withhold tax for a different state for just one employee. If the employer is offering to withhold Kansas tax, they may already have other employees in Kansas. They might have some sort of operations in Kansas, even if they don't have an office there.
You will not have to pay New York City income tax under any circumstances.
"Nonresidents of New York City are not liable for New York City personal income tax."
https://www.tax.ny.gov/pit/file/nonresident-faqs.htm#nyc
Years ago nonresidents of New York City who worked in the city had to pay city income tax. Through litigation and legislation it has been established that New York City cannot tax the income of nonresidents, even if they work in the city. This has been the case since 1999.
