On the other hand, lower interest rates allow banks to synthetically create more money at a lower cost (e.g. corporations borrowing say, a million dollars at 1% interest is very attractive) and that will drive inflation more broadly, because its new money created. Raising rates makes creating money more expensive (setting a higher "floor" on the price of new money relative to what the banks get it at)
This is why interest rates rising in theory, will depress housing prices because it costs more in monthly payments to cover the interest on the mortgage to buy the house, which means fewer people can buy more expensive homes and it takes more money out of the economy as a result, because borrowing is more expensive. This is why you can get 5% yield CDs at banks quite suddenly, because giving you favorable terms on savings is cheaper than borrowing the money from the central bank.
Its false equivalency to think cash assistance and many other forms of social welfare drives inflation more broadly, in the general case.
I will caveat there are specific cases where inflation can be driven by government spending directly, but its not generally the case with things like cash assistance, in due part because its not creating new money.
[0]: I'd like to just point out, I'm explaining a very complex system of inputs and outputs in very simplistic terms. While its not incorrect per se, it certainly is more complex than I'm laying out in reality. Conceptually however, I think this explanation is rather sufficient in getting the point across that I'm asserting
[1]: if I'm wrong, I'd love for someone to point out what I'm wrong about. I'm assuming most of us aren't economics majors here, therefore, as noted, I omitted alot of nuance, while acknowledging that there are cases where the government can cause inflation via spending.