@Sheldon points out
I think it's been 20 years since the last contact with Pioneer10, but I assume these numbers are nonetheless very accurate
The blurb in the Horizons output for Pioneer 10 says:
The last fully successful acquisition of signal was March 3, 2002. Pioneer 10 signal at the Earth (<= 185 dBm) is now at DSN threshold limit of reception.
With that important caveat in mind, we can still look at the trajectories in Horizons which will be based on all observations of the spacecraft and an excellent model of the solar system's gravity. Barring some unknown venting events or new Pioneer anomalies, these should be pretty accurate.
The crossover for distance to the Sun (which moves around a bit relative to the solar system barycenter due to mostly Jupiter, Saturn, Neptune and Uranus, in order of decreasing effect) was roughly at about
2023-Jul-18 14:00 UTC at about 20.0343 billion km, and for the distance to the solar system barycenter it came a day earlier at about
2023-Jul-17 15:00 at about 20.0328 billion km.