To whit, US mortgage debt in 2020 was at $10T while the debt that the poor are more likely to have (Credit Card / Personal Loan / Auto Loan) is a combined $2.5T[1].
The wealthy are often highly leveraged in a variety of ways. Just look at some of the world's richest people – they generally fund themselves through loans taken out against their equity holdings (stocks in the case of Bezos / Musk / etc).
So the ultra-wealthy like Musk are actually winning twice: once when everyone rushes to buy stocks like Tesla because they're worried about inflation and such, increasing the value of his holdings substantially. Then again when the inflation actually hits, because he is funding himself with loans, which are now easier to repay.
[1] https://www.experian.com/blogs/ask-experian/research/consume...
Wages for the poor won't go up because they don't have any leverage in terms of negotiating. With no fixed assets and no negotiating power to demand higher wages, the value of the real payback won't change for them, but the cost of living will go up.
It'll help a few people who got lucky and bought houses within the last couple of years, but the truly poor (no assets) are about to get much poorer in terms of purchasing power.
The poor tend to be net borrowers. The rich tend to be net lenders. Inflation makes the poor less in debt by lowering the real value of payback. Inflation helps borrowers.