Civilians think unemployment means people don't have a job. Reality is its a measure designed in the 30s and heavily gamed and politicized to not mean very much.
A somewhat more realistic measure would be something like FREDs EM ratio. About a decade ago 62% of the population was employed, and after the great recession we've slowly climbed back up to 60%. Flat at 58% from the great recession until 2014, then continuous growth since. Sure theres boomers dying off, but that means demand dying off too, in theory the ratio should be fairly constant. FRED is an online product of the St Louis Federal Reserve; at least semi-trustworthy, surely more trustworth than unemployment stats.
Its not so much intentional dishonest as changing the definitions of what it means to be unemployed with all kinds of moral and ethical boundaries for welfare services etc. On the other hand, the percentage employed is reported honestly as a simple percentage of the population with a job. To have a job is a honest observational result; to be in the legal and welfare state of qualifying for unemployment benefits is a totally different kind of subjective observation. We could have 0% unemployment simply by not providing benefits anymore, which is kinda what we're doing.
Anyway the point is the last time the employment percentage was as low as 60% was after the 1983 recession; the graph is surprisingly not very dramatic and the percentage of employed americans post WWII has never been below 55% and never above 65%. None the less, the current stat of 60% is 3% below the peak in '07, almost 5% below the peak in '99, 3% below the peak in '90... For most of the 80s, all of the 90s, all of the 00s, employment was higher than it is now. Admittedly its better now than at the end of '09, but hardly at a high number.
As such, given that about 3% of the population was very recently working and now is not, we have a long way to go before any wage pressure.