The government claims that this high CPI is due to Russia's invasion of Ukraine (you could argue that, one of the reasons is the sanctions on Russia's economy, which don't do much to harm to the Russian government and hurts ordinary people both inside and outside Russia). But this is just an excuse for the government to not admit the blame. It is clear the war has an influence on the CPI, as it eliminates the supply of various goods and services, which ends up increasing prices. However, the CPI has been going up since February 2021.

The 2020 and 2021 lockdowns (and the followed supply shocks) were also a big factor, but the real reason prices are going up is the inflation (monetary expansion) created by the US government both in 2020 and 2021.

Yes, supply shocks cause increases in SOME prices in the economy, but not a general increase in the prices of goods and services. If there is a supply shock of certain goods (making their prices higher), but the money supply does not change, there will be a new equilibrium of supply and demand for the various goods and services in the economy (since the money supply is the same and individuals will have to change the allocation of their budget, so the prices of the goods that will have a lower demand will decrease).