Core PCE includes food (split between line 9 and line 19), and fuel (line 11).
These are things you can easily google. The composition of the PCE, CPI, and other metrics is public information and publicly documented.
> The Fed only sees no inflation regardless of the inflation we see all around us.
Both CPI and PCE are both up slightly in the past year. Both are measures of inflation and clearly indicate slightly higher prices.