There isn't one unemployment rate in the U.S., there are actually 6. What the news usually calls the unemployment rate is the U3 rate. [0] You're suggesting the U6 is a better measure, which makes sense to me, but I'm not an economist.

What I've read recently though, is that workers' expectations of inflation also play a big role in inflation. [1] The idea is that low unemployment means workers are confident and have leverage to demand pay raises that meet their inflation expectations. We may have broken inflation expectations. The Brazilians did an amazing psychological hack with the creation of the Real to fix their inflation expectations to get their inflation in check. (Though, they had the opposite problem, workers expecting very high inflation.)

[0] https://www.investopedia.com/articles/investing/080415/true-...

[1] https://www.economist.com/schools-brief/2020/08/22/why-does-...