Prices are governed by supply and demand. If you do boycott and therefore reduce demand, prices will drop. However, if the price drops to a level lower than whatever it cost to produce it, producers will not be able to afford to make it so will (assuming that they can't cut the cost of production) cut the number of goods produced and this will make the price rise again.
Take vegetables. Farmers are under a lot of pressure from supermarkets and their margins are wafer-thin. They can't cut the cost of production because fertiliser manufacturers cannot afford to produce it for less than it cost them to buy gas and turn it into fertiliser. If a farmer cannot get a good price for his vegetables, they will just be left to rot in the fields because it is cheaper than paying someone to pick it and sell it at a loss.
The one commodity that is at the base of all this is gas. We use natural gas to make fertiliser, which helps us produce food. We also use it to generate about 40% of our electricity so if the price of gas spikes, so does the price of electricity.
Firstly when we were using less energy during the pandemic production dropped to match, then as lockdown ended production struggled to catch up, so prices rose. When European countries panicked last year and paid over the odds to make sure that their reserves were full before the winter, without using Russian gas, the price shot up to a high of £640/thm in late August 2022, before dropping once reserves were full and demand therefore stabilised.
For context - just to show how big an increase £640/thm was - before the price started rising in summer 2021 when lockdowns ended, the highest recorded wholesale gas price in history was £110/thm in 2005, it spent most of the 2010s around £75/thm. We had a fairly mild winter so Putin's plan of freezing ourselves into submission didn't work, and Europe's gas reserves were easily replenished. Wholesale gas prices therefore decreased steadily to £100/thm. I'm on an agile electricity tariff and have certainly noticed prices dropping.
So the answer to getting prices down is to not have our energy supplies in the grip of hostile dictatorships. Not just Putin's gas, I'm also referring to Arabian oil - we are very dependant upon crude oil, the tractors, harvesters, and lorries that bring food from the fields to your supermarket all run on diesel so if the price of oil goes up, so does the price of food.
We need to invest in a nuclear power baseload and supplement it with renewables, building interconnectors to balance the peaks and troughs in renewable generation across Europe. Would you believe that while they were considering blackouts in the South East of England due to high demand, they were simultaneously paying Scottish wind farms to switch off? The reason is that we haven't built enough transmission capacity to take the energy to where it is needed.
Until then, fossil fuels are the ones to boycott. Even if the price doesn't go down (because the OPEC cartel will just cut production), you are still saving money and helping the planet in the process.