Right off the bat, we should establish that Code: White is an original story, not adapted from the Spy x Family manga like the TV series is.
If you can accept that Code: White is, in effect, an extra-long Christmas episode of the Spy x Family TV series with a bigger budget, there’s a lot of heartwarming fun to be had.
With the manga itself ongoing, and quite a bit ahead of the TV series, that makes Code: White a Spy x Family side story, or gaiden, if you want to use a Japanese term…or a filler story, if you want to be harsh.
We know there are more Spy x Family manga chapters and TV episodes to come, and there’s no Spy x Family without the characters being a family.