DANGEROUS_PROXIMITY distance not always honored (save included)

### Describe the bug

Sometimes the dangerously close message happens too late after you hit I or N in the monster spotted dialog window, the Zed is in a nearby square.
From _Originally posted by @Cenness in https://github.com/CleverRaven/Cataclysm-DDA/issues/63965#issuecomment-1455594230_
`
static constexpr int DANGEROUS_PROXIMITY = 5; `
it looks like the distance is hard coded at 5 at the moment but in the save attached, the monster ends at a distance of 1. (5 is fine btw).

### Attach save file

Trimmed save
[Usher-trimmed.tar.gz](https://github.com/CleverRaven/Cataclysm-DDA/files/10910123/Usher-trimmed.tar.gz)

Full save in zip format is here (80MB) if the trimmed one does not work for you :
https://1drv.ms/u/s!AgU0TIkDwXcdhI1fx9ARYGah1SudJw?e=sIMC0z

### Steps to reproduce

Ok, I managed to reproduce it:
In the save attached:

1. hit | (wait) then w wait a while then choose wait 1 minute at least
2. Popup window: "Police bot spotted" answer I (ignore)
3. Popup window: "The police bot is dangerously close" answer Y to cancel waiting
4. the bot is in the adjacent square and NOT 5 squares away

### Expected behavior

Player should be able to react when the monster crosses the DANGEROUS_PROXIMITY distance (5 atm) and NOT when the monster is 1 square away.

### Screenshots

_No response_

### Versions and configuration

- OS: Linux
- OS Version: LSB Version: core-11.1.0ubuntu4-noarch:printing-11.1.0ubuntu4-noarch:security-11.1.0ubuntu4-noarch; Distributor ID: Ubuntu; Description: Ubuntu 22.04.2 LTS; Release: 22.04; Codename: jammy;
- Game Version: 7762a54 [64-bit]
- Graphics Version: Tiles
- Game Language: English [en]
- Mods loaded: [
Dark Days Ahead [dda],
Disable NPC Needs [no_npc_food],
No Fungal Growth [no_fungal_growth],
Stats Through Skills [StatsThroughSkills],
Alternative Map Key [alt_map_key],
Bionic Professions [package_bionic_professions]
]

### Additional context

_No response_

Start by reproducing the attached save and trace the handling of the DANGEROUS_PROXIMITY constant during the monster-spotted dialog and waiting flow. Done means the player can react when the monster crosses the configured five-square distance, including when waiting is interrupted or the game is saved.

Written by the indexing model from the issue text.