We are not seeing rising prices of food and consumer goods now because people were given these checks in lieu of working as that money simply replaced the money they would have earned for the most part. In economics inflation is defined as an increase in the supply of money, so this is actually not inflation because there is no new money in the system but rather only a change in the source of that money, namely the government. Prices are going up now because of interruptions in the supply chain, which are purposeful and designed to create chaos, and because the people that were laid off and are now receiving government checks are no longer producing goods and services and therefore there are less of each to go around.

Yes, governments that are indebted to their own citizens through the issuance of domestic government bonds usually end up paying that back through the use of inflation. However, it has to be remembered that government-issued bonds are not secured debt and that a government can simply declare bankruptcy and wipe out all of those bonds at the stroke of a pen without anybody having any sort of legal claim to anything to make up for that. The only penalty that would be paid in such a case is that such a country would be shut out of the international debt markets and likely would not find buyers for their domestic bonds either because of the breach of trust of not meeting previous obligations of paying back borrowed money.