Empty coolchat not created when making new characters

[Aphast]

---- Testmerges: ----
Round ID: 54
BYOND Version: 515.1641
Server revision compiled on: 2024-12-02T17:32:36+00:00
Master commit: a347d6a1f42b5806c7dbdf75e4d751a9b03a60c9
TGS version: 5.2.4
DMAPI version: 5.9.0

Current Informational Settings:
Protect Authority Roles From Traitor: 0
Protect Assistant Role From Traitor: 0
Enforce Human Authority: 0
Allow Latejoin Antagonists: 1

---- Reproduction: ----
Setup 1 character's coolchat, pics, etc.
Create a new character and notice it shares the same stats as the previous character where it will then require full removal of all previous links rather than having the default template.

---- Screenshots: ----
Mouse is currently broken, snapshots unable to be properly made, issue is reproduceable enough

---- Additional context: ----