That kind-of works, the changelings all modelled their looks on Odo's, which was modelled on a Bajoran, so maybe when they need to replicate buckets out in the field, they go with the same style as his
was just a callback/easteregg for DS9 fans, but if there is a story reason for it, it might also be symbolic to the Rogue Changlings:
When Odo joined the Great Link for good, he probably also shared his experiences with the bucket. The bucket represents a time where he was arguably still the most isolated from everyone around him, and from his people. And when shapechanging was part of the job, but not a fun experience to explore or take joy in.
Only when he grew closer to the crew, and when he learned more about his people did he abandon it, started having his own room with shapeshifting "toys" to explore his ability.
The rogue Changlings are isolated from the Great Link too, and for them, shapechanging right now is a job, something they must do to accomplish their goals, not for the fun of it. Unlike Odo, they'll never make the mistake of falling in love with Solids (at least that's what they believe), but very much like Odo, they seek to return home one day, when they have done what they need to do. The Bucket is a symbol of what they are right now, but also a warning that it will be the rest of their existence if they fail.