Gas prices are significantly higher than 2019, total vehicle miles travelled are about the same (https://fred.stlouisfed.org/series/M12MTVUSM227NFWA) so there must be a reduction in supply or just straight price gouging to justify the price increase.
There are both supply shocks and demand shocks. Gas prices are definitely undergoing a supply shock right now, which contributes to the price increases (and which the Fed can't help.) But there are also broad-based demand increases.
I agree with your first statement but per the data on aggregate miles travelled I disagree there's actually a demand increase. Ultimately the Fed can't control either supply or demand directly but they try to indirectly control demand by increasing the cost of borrowing. Will it work? Consult your magic 8 ball.
My statement about demand and supply shock is about the broader economy. Gas price is not the only indicator or driver of inflation.
In the case of gas, supply issues predominate, although it is worth noting that price of gas going up and number of miles staying the same indicates both supply and demand shocks at the same time.
The Fed has almost perfect control of aggregate demand. Inflation is more challenging because it bakes in expectations.