There is no great distinction made between display and internal logic other than to note it means you continue the search, or rerun it to find another variable (including assuming it is some kind of anti cheat method in play* and adjusting accordingly -- skip the specific numbers and if less than searches and go for thing changed, maybe a few rounds of stayed the same, restart a level maybe...).
*if the motion of throwing a grenade is decoupled from the underlying value in such a manner it is a fairly safe assumption it anti cheat of some form -- for an action as presumably irregular and not necessarily time sensitive as most grenade chucking then no great benefit to having the value live somewhere else for quick reference, something we sometimes see for health and other values that are always referenced and maybe demand a more immediate response.
The only real benefit to having the display value is whatever changes that will at some point along the path. To that end if you wanted to conduct a tracing session (
https://www.romhacking.net/documents/361/ is for the GBA and graphics searching but the principles apply everywhere, main difference being here you likely have pointers to deal with) then you have something to set a break on read/break on write to and follow back up the chain or onwards to whatever. At the same time though you could also just key off a button press which is likely to be even closer to the source.
Only other thing I would note at this point is if any other cheats have been made for the game it could be worth analysing those (possibly also making the naive cheat for what they are responsible for) to see if they provide a glimpse as to the nature of anti cheat in this game, or even maybe the location (if ammo and a bunch of other variables exist in a temporary location or are obscured in some manner then chances are they are all nearby or using similar methods).
Alternative some opt for if the searches don't work and tracing is too annoying then if there is an alternative means (pickup, potion, level up, death but give the player back a life, fake being some kind of recharge point in a level... it is all very game dependent) then see about sorting that with a cheat.