Q: What is the highest apogee of a satellite in Earth orbit they need to avoid? Ignore any satellites in Solar or lunar orbit.

A: There are over a hundred satellites in Molniya orbit, a few tens in Tundra orbit and a handful in really high earth orbits. The first two of those go above geostationary orbit; there are examples of the last with perigee of at least 375,000km. //

James Webb Space Telescope, at the Earth-Sun L2 point, is roundly a million miles from Earth, but still gravitationally bound to the Earth-Moon system.

Other than that, there are very few if any permanent satellites beyond the "graveyard orbits" used to park expired geostationary satellites. These are typically only a few hundred kilometers higher than geosynchronous, however, so roundly if they're well beyond the 24 hour orbital period, they'd be well clear of anything we put up intentionally and left there. //

Then there is stuff, mostly debris, that is more critical, because by nature those pieces are very fast, the orbit is not stable, so it changes a little every round and the kinetic energy would be able to penetrate any hull that is not specifically designed to withstand such impacts. For example, this debris of an Iridium satellite - at the time of writing at altitude ~366,000km and counting, spiralling outwards at 1km/s (the map does not mention a size or weight though. But it is big enough to be trackable obviously).