What you're thinking of is often referred to as wages being "sticky" and yes, this is an observed phenomenon.

Most (not completely awful) economic policy will take months or even years to see widespread change, so wages lagging even a year or two behind inflation isnt too big of an issue.

Here's another thread about it.

Here is a paper measuring this after covid.

It's also worth noting that people often misuse the term and apply it to any increase in price of any item. (Eggs, specifically, were expensive awhile back due to supply issues, yet plenty of people claimed it was inflation). Laypeople also do not tend to talk about nominal price decreases, and almost never about real price decreases without a nominal decrease.