I think the two best candidates would be what the next CPI estimate will be and what the next inflation expectation estimate will be.

CPI estimates are put out by the bureau of labor statistics (https://www.bls.gov/cpi/) and the next one comes out 10/15. You'd just have to specify overall vs core inflation.

Inflation expectations are gathered by several groups. I think the most cited come from University of Michigan and can be tracked at the Federal Reserve (https://fred.stlouisfed.org/series/MICH). They survey both one-year and five-year expectations. I think one-year is probably the better choice. The next release is 10/24.

I'd lean towards overall CPI as the inflation market of most interest to folks.