How Is Our Current State Different from What We Would See in a Successful Inflation Soft Landing?

It isn't. It isn't different at all...

What would a soft landing with respect to inflation have looked like?

Perhaps like this{

Look at the core inflation—the CPI excluding fluctuations in volatile food and energy prices (and do recall that core inflation is a much better forecast of future headline (and core) inflation then current headline inflation is).

For the last three months core inflation has been at the Federal Reserve’s target.

CPI core inflation has been running at 2.5%/year. When you take account of the persistent wedge between the CPI and the PCE index that is the Federal Reserve’s preferred target measure, that is what is needed to get 2%/year PCE chain-index inflation. If recent-past core inflation turns out this time to be a good forecast of future inflation, then the inflation burst that started in 2021 will be adjudged in the future as “transitory”, and extended beyond its natural reopening-period length by the supply shock delivered by Vladimir Putin’s attack on Ukraine.

There are only two reasons in the tracks of the time series itself to doubt the forecast of a soft inflation landing: