That was a specialty pre-production version of the F15 that was modified to do basically just altitude and speed records. It never entered operational service.
The service ceiling is published as FL650. That’s defined as being able to sustain a 100fpm climb, so the absolute level flight ceiling is somewhat higher than that. Service ceiling figure is not in a zoom climb.
It would easily suffice to engage a balloon at FL600.
the venerable english electric lightning (RAF) intercepted a u2 at 66k feet during a nato exercise under full control. it also made it to 86K feet, but that was a zoom climb, and the pilot seems to have found the experience rather scary.
https://theaviationgeekclub.com/how-the-f-15-streak-eagle-br...