The short answer is that there is very little you can do from the outside to change this, and understanding why helps make sense of what feels like an overreaction.
Once a flag exists in someone's record indicating a prior suicide risk statement, even something said offhandedly during a stressful arrest years ago, it follows them through the system. Every time they enter a new facility, intake staff reviews that history and makes a precautionary placement decision based on what is documented, not on what you or your son says today. From the facility's perspective, they are managing liability and acting in what they believe is his best interest. A death in custody is the worst possible outcome for everyone, and they would rather err heavily on the side of caution.
That does not make it less frustrating when the flag no longer reflects reality.
The path forward has to come from your son's side, not yours. While he is on suicide watch he should be evaluated by the facility's mental health staff. That evaluation is the mechanism through which the watch gets lifted. If he is calm, cooperative, and clearly not in crisis, a mental health professional at the facility can clear him and have him moved back to general population. The key is that he needs to engage with that process directly and honestly rather than expressing frustration about being there, which can inadvertently extend the placement.
On the longer term, his attorney can request that his mental health records be reviewed and that the flag in his file be formally reassessed. A current evaluation from an outside mental health professional documenting that he does not present a suicide risk can be submitted to the court and may help prevent automatic placement in future incarcerations.