Text on signs shows different colors if dyed manually or by command

The bug

Colored text on signs has a different color if set by json in a command (/data or /setblock) and a different color if dyed manually using a dye. If this is intentional design and not a bug, it might be worth to say that the color of text dyed using a dye is often unreadable. Attached is a picture comparing the two cases.

How to reproduce

1. /setblock ~ ~ ~ oak_sign{Text1:"{\"text\":\"test\",\"color\":\"gray\"}"}
   

2. Place a sign, write on it and dye it with gray dye
   The text color of the signs is not the same