I think stigma related to receiving psychological and psychiatric services will exist as long as nonconsensual psychiatry exists.
Once suicide is respected as a civil and human right for adults then people will be able to have open and honest conversations about suicide in private without being concerned about potentially being locked up in a psychiatric unit. Additionally once suicide is respected as a civil and human right for adults then I think fewer people will attempt to engage in suicide unless they are actually and definitely wanting to die (rather than as “a cry for help”).
I encourage you to read the books Suicide Prohibition and Fatal Freedom; both were written by psychiatrist Thomas Szasz.