"Launches to higher-orbits have included DSCOVR to Sun–Earth Lagrange point L1, TESS to a lunar flyby, a Tesla Roadster demonstration payload to a heliocentric orbit extending past the orbit of Mars, DART to the asteroid Didymos, Euclid to Sun-Earth Lagrange point L2, and Psyche to the asteroid 16 Psyche." Per wikipedia, not sure if those count as meaningful. Plus Europe Clipper in a few months.

If you mean human spaceflight, current Boeing has less experience flying humans to anywhere in space than SpaceX, let alone beyond low earth orbit. If you mean general spaceflight, SpaceX has launched more lunar and interplanetary payloads than Boeing has in the past decade or two.

Boeing and its proponents love to talk about things like "spaceflight heritage", but none of that means anything when most if not all of those employees are gone and nothing was done to transfer the knowledge.

They regularly have missions to Geostationary Transfer Orbit, but I assume that’s not what you’re talking about.

Not yet, but I believe the Artemis 3 manned moon landing is still a planned for 2026.