cmd.exe ignoring /t color when using /c instead of /k

Let's say I have a simple .bat file called foo.bat containing just

@echo off:dostuffecho bartimeout /t 2 /nobreakgoto :dostuff

If I run it from prompt Microsoft Windows [Version 10.0.22621.3155] with start cmd.exe /t:04 /k foo.bat then a terminal will open with a black background and red text

If I run it with start cmd.exe /t:04 /c foo.bat a normal black background and white text prompt opens.

I haven't seen any mention in Microsoft's documentation that /t is not supported by /c, is there a way to have the same color behavior as with /k?