I think Fallout 4 handled the balance of movement speed and sprint well for an open-world setting. Players still maintained a fast base movement speed comparable to Fallout 3 or New Vegas, but added a Sprint function that tied into the VATS mode, which is not necessarily essential, but still a staple of Fallout's gameplay. Level design was not impacted by Sprint this way since players would want to save their AP to use in VATS, keeping levels tights and manageable without needing to use Sprint; I rarely Sprint anyway when playing Fallout 4. If Halo Infinite were to keep some variation of Halo 5's enhanced mobility mechanic, I think it would be wise to tie Sprint to the other Thruster-based abilities in a similar fashion. So when traversing the possible "open-world" of Infinite, players could utilize Sprint during periods of downtime, but then save the "AP" for combat encounters that do don't factor in Sprint, since players won't be using it.
The multiplayer competent could work in a similar fashion if Sprint even remains in there; an argument could be made since that Arena consists of purely arena-based maps, there would be no need to incorporate Sprint there since movement speeds and Thrust would be more than enough to suffice in the tighter space. It could be incorporated in bigger modes like BTB or Warzone (if that even returns), as well as if the open-world becomes a shared space. And even if Sprint were to remain in Arena, it's effects would be seriously reduced to the point where it becomes an even riskier option for such tight combat. For example, if a player decides to sprint around the map, then they will drain their "AP," making them more vulnerable in a gunfight since they will not be able to use their Thrusters as much, if even at all. And if they are losing a gunfight and have barely or no "AP" left, then escaping will not be a viable option unless they can get away naturally and survive long enough to charge their "AP" to make a successful getaway. Or let's say the player is hit by a weapon that drops their shields completely before they use any of their "AP" like the Sniper Rifle. The player will then be able to use it as a last resort "panic button" and use Sprint as a tradeoff mechanic to find cover faster so they can wait to recharge their shields like they would have to in Halo 5, assuming they don't get killed while fleeing by a follow up shot. Also, maybe EMP-based weapons like the Plasma Pistol could drain "AP" as well, and if that proves to be too OP then a new weapon could even be made that can drain "AP" somehow.
Overall, I think that this would be the best way to implement Sprint because it fits the mechanic into the Halo sandbox without effecting anything, but instead improving one of the drawback of some of Halo's design issues when spaces get to large without any vehicles around, such as in a BTB map like Blood Gulch or a mission like Assault on the Control Room. However, tying Sprint to Thrusters via an AP-like system will create a greater consequence for this action, so while it becomes viable in situations where the level design does not allow the player to engage in combat effectively or even at all (such as just roaming around), Sprint becomes the best ability to commit your "AP" to since it will be of actual use, but when combat picks up in close quarters, that "AP" will need to be used elsewhere. Sure, there will be some times where Sprint will still be an annoying feature, like if a player actually manages to escapes fair fight with it somehow, or if a player with longer-ranged weaponry does not need to use Thrusters as much and can therefore reposition themselves faster with Sprint (although some people might actually like that element to balancing the abilities with gunplay), but overall it will be much more tastefully implemented than in Reach, 4, or 5.
