You are correct that unemployment rate is an indicator which reflects the overall health of economy, how lower unemployment rate rate can directly impact inflation as it can create upwards pressure on wages as employers complete for a smaller pools of available workers.
Someone has been learning! You're just one of the very few in the forum who truly got the concept. The majority of people have been gaslighted by the misinformation and gaslighting being spread in the media.
Inflation is a complex economic phenomenon, that can be influenced by many factors, but I think oil price play main role in its escalation. therefore, if oil prices were start to falling significantly, it could potentially ease inflationary pressure and lead to a pause in interest rates increase.
It's a MONETARY phenomenon. The "supply side inflation" narrative doesn't explain why inflation is sticky. Simple good sense will tell us that if there's too much money in circulation = more demand.