your points are valid, but leave out some important effects.
the reason lower rates can trigger high inflation is because lower rates cut costs for consumers, who can then consume more (increased demand). companies can borrow more cheaply and can therefore expand to meet the demand.
because the market change is led by consumers willing to spend more, there is generally a market adjustment in the form of higher prices (increased inflation), especially if the supply side is slow to meet the increased demand.
this increased inflation does lower demand, but the effect is nearly always smaller than the original increase in demand caused by the lower borrowing costs.
this is why lower interest rates generally stimulate the economy but can lead to (usually slightly) higher inflation.
now, there are always exceptions. say the economy is already red-hot and the supply side really can't expand to meet the increased demand. well, then the extra spending money in consumers' hands just goes to raise prices, so then, yes, you have more inflation than usual and little increase in gdp.
conversely, if people completely lose confidence in the fed because they cut rates way too much, enough to trigger spiraling inflation, then yes, that effect could become larger than the original effect of increased demand. but in order for that to happen, there has to be a self-sustaining mechanism for inflation to spiral. that's hard to happen without a strong labor market that is capable of getting pay increases, and usually that means strong unions.
we definitely don't have strong unions these days, though there have been some gains under biden in terms of wage increases. that said, i really doubt that will continue under donnie.
all in all, i think we're likely to be in a relatively typical economy where the fed lowering interest rates too much would stimulate the economy (higher gdp), but with a certain amount of increased inflation.
if the higher inflation is neglected for long enough, then people will lose confidence in the fed, which *could* lead to the spiraling situation described above that could eventually lead to a recession. but i think it's more likely that we still have modest growth with high inflation.
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