I'm skeptical of this narrative. I'll bet MLSE would be just as happy to have given Ujiri whatever he wanted to have that foundational stability simultaneously as he's working out these negotiations for his underlings. The way MLSE throws money at staff and players, they would have surely given the championship front off, Nurse and Webster whatever they wanted without too much of a delay. In terms of appearing to be relaxed and in no hurry to re-sign, that feels like the stance of a person who is eager to explore all of his options, not commitment.
Anyway, Ujiri has every right to do whatever he wants but generally the slow roll to free agency and out the door is usually one of the more painful sports breakups to witness. It would be like the executive version of the current Giannis storyline and the previous Kawhi storyline, so hopefully I'm wrong on this one.