BEA's news report:
https://www.bea.gov/index.php/news/2024/personal-income-and-outlays-april-2024
Source of index values to produce the graphs:
PCE: https://fred.stlouisfed.org/series/PCEPI
CORE PCE: https://fred.stlouisfed.org/series/PCEPILFE
PCE (3 month and month-by-month) Thru April'24, 5/31/24:

CORE PCE (3 month and month-by-month) Thru April'24, 5/31/24:
(The Fed's favorite inflation gauge for projecting FUTURE inflation)

https://finance.yahoo.com/news/new-inflation-reading-reinforces-feds-higher-for-longer-stance-144840988.html
Fed Chair Jay Powell warned about today's PCE reading on April 16, saying he didnt expect it to show progress and that measures of inflation on a three- and six-month basis are now more elevated.
(emphasis added)
That was a month and a half ago. With the horribly high January dropping out of the 3-month window and today's moderate April-over-March readings of PCE: +0.257% (3.12% annualized), and CORE PCE:+0.249% (3.03% annualized), there's a nice downturn in all of the graphs
Still, the latest 3 month averages, annualized are PCE: 3.80% and CORE PCE: 3.46%. But it's headed in the right direction.