When I say mission, I specifically mean the mission in the form of Artemis, not a permanent human presence on the Moon. The latter doesn't require three brand new rocket systems, especially not a Shuttle derived one.
SLS was created to keep job in the states that had STS facilities and needed Shuttle tech to justify their continued existence.
SpaceX HLS was just as questionable. Competitors presented realistic timelines and budgets, while a single person at NASA on her own decided to exploit the power vacuum after an administration change to award the only contract to SpaceX only to be hired by them shortly after.
The mission is not to develop a rocket that can deploy StarLink 2.0 satellites or supposedly take people to Mars. The mission is also NOT to keep engineers who worked on Shuttle employed. That's the issue and that's the problem with Artemis.
As far as new technology is concerned - you focus on tech required for the mission: new and more capable space suits (in the works), a more capable vehicle (Orion), reliable long term power delivery (NASA's KiloPower reactors), a logistics hub (Lunar gateway), communication systems (relay satellites), new surface capabilities (contract signed with JAXA), etc.
If you really want to achieve a goal, like giving NASA some new focus and establish a permanent presence on the Moon, you take the lessons from the past and improve upon them. A shoestring budget, a needlessly expensive new launch system that only exists to keep jobs and reliance on high risk new technologies without proper justification aren't it.