NASA has taken a cautiously optimistic stance on Starship. The assignment of the HLS to Starship and no other provider was an aggressively optimistic stance from NASA that surprised many of the space industry observers at the time of its announcement. The expectation (and normal NASA behavior) would've been two assign the HLS to multiple vendors, at a reduced funding level and stretch the timelines out.
So, I'd argue that NASA is already being quite bullish on Starship given the projects and funding that they have available.
But then, I know nothing about how NASA operates internally.
Trying to a void a lawsuit is how you get nonsense like the LCS where the Navy first opened the bids for a single class of ship, and then when it was time to announce the winner, split the contract between Marinette Marine and Austal.
You have it backward. Airbus won the contract initially. Boeing sued and managed to get the bidding process restarted from scratch. Boeing won that second bid and Airbus decided to not protest, probably because they knew they had 0 chance against Boeing lobbying power in the US.
For example, NASA could start allocating a small-ish budget (e.g. 50M$) to design a parallel mission to their Artemis-IV mission that is currently scheduled for 2026 (but will slip) and that should deliver the Gateway i-HAB module to Moon's orbit.
While 50M$ (excluding launch costs) for a mission like this would be lunacy today given the constraints on weight imposed by current rockets, with Starship that would be a sizeable budget to design a much bigger and more useful module.
If by some cut-off date (say 2024) Starship still hasn't proven itself, then scrap that mission, proceed with the original one and the wasted 50M$ will be a rounding error in Artemis-IV budget.
If Starship proves itself before then, scrap the original mission and go with the redesigned Artemis-IV based on Starship. Billions of dollars will be saved (SLS launch cost + at least 2 years worth of development), and we will have a Lunar Gateway 10 years ahead of what we would have had otherwise in terms of capabilities.