I also think the increased money supply has an effect. However, I'm not sure of the mechanism from this to the price increases.
More competition at the market. More demand. If you are bidding for a product or a service and there are more people bidding, the higher the cost.
Imagine an auction. You have the usual crowd every week and prices generally stable. Now double the crowd because people now have more money to spend. Now prices increase because people are competing for the same amount of supplies.
The example you give of more people chasing the same goods is fine with the conventional definition of supply and demand. I have to agree.
Except - I don't see more real competition by more people. I see price rises due to some shortages, but do we have a true increased demand for the butter and egg type products. People are still eating as they were before. I assume many are still working at home which would lower demand for some products and raise demand for others You can cherry pick, but is there an overall increase in demand?
Now the part I truly don't understand about the increase in the money supply is how this extra money gets to John or Jane Doe so they have more money to spend and then are able to stimulate demand. There may have been slight increases in wages, but I think they have been largely stagnant. There has been some government assistance, but has it been significant enough to bump inflation. I guess I don't seen the people being the beneficiaries of this increase in money supply. This is what I mean when I say I don't understand the mechanism as to how this money reaches the people.
Inflation is increasing due to multiple factors. Higher wages are one aspect. If a burger flipper is paid $15/hour instead of $10/hour then McDonald's will raise the cost of a hamburger $0.50-$1.00 as that will allow them to maintain the same profit margin given higher costs. Those higher wages are due to a labor shortage which is partly due to the pandemic and partly due to government subsidies allowing others to leave the labor market. If you were making $1,500/month and paying $1,000/month for daycare you're effectively making $500. When all of the sudden you start getting $300/month from a child tax credit you're looking at effectively making just $200/month instead of $500/month if you stayed home instead of going to work and sending your kids to daycare. If the daycare raised their prices to $1,100/month the decision becomes even easier. A lot of people left the labor force because it's either not cost effective, or they can't get child care, or they don't want to risk getting sick, or they just retired early when they got sick of dealing with the BS and realized they had the money to stop working.
Then you have other increased costs like food. Food costs are going up because of labor shortages, higher energy prices, and higher input costs - such as fertilizer. Nitrogen-based fertilizer is primarily made from natural gas. In Europe for instance the cost of natural gas has risen from approximately $20 euros to $100-120 euros. About 80% of the cost of nitrogen-based fertilizer is from the cost of natural gas so a 5x increase in the input cost means nearly the same rise in the price of fertilizer. That means next year either crop yields will be lower (lower supply and fixed demand = higher prices) or the cost to produce the same amount of food will go up which will also mean higher prices. The dynamics are a bit different in the US, but fertilizer is a global market. So some of the fertilizer made in the US is now going to get shipped to Europe where prices are higher which means less supply in the US and therefore higher prices.
There are also higher prices due to higher shipping costs. The cost to get a shipping container from the east coast of China to the west coast of the US pre-pandemic was about $3-5k. Most of 2021 that's been $15-25k. If that container has $50k worth of goods you've effectively increased the cost of those goods to retailers by 30%+. Most retailers sell at 2-4x the cost of goods so a product that cost them $10 to manufacturer in China and get shipped to the US will sell for $20-40. If that cost goes up to $13 they're going to raise the price to $26 - $52. Maybe not immediately, but eventually everyone along the supply chain raises their price and it finally gets to the end consumer.
My household received almost $20k in "free money" since the pandemic began. With an annual household income in the high five figures that means an effective 10% increase in earnings. It's pretty obvious if you drive by an auto dealership where a lot of that money went. Between the chip shortages (lower supply) and that increased demand you get higher prices. Most people will spend all their money. When services (restaurants, live entertainment, etc.) become unavailable that money flowed into goods. The supply chain couldn't handle the increased demand and we're seeing all the second- and third-order effects now.