Moreover, what exactly would she be tried for? Do we need a trial to establish that she has in fact continued to disobey the judge's order to unlock the phone?
The courts really don't get to hold someone indefinitely without charging them with something.
Contempt is generally used as a quick and dirty hack for someone disobeying the procedures of the court. Not providing a fingerprint to unlock evidence is WAY beyond that scope and probably should require a hearing and trial.
Now, she could be detained while that hearing is proceeding, but that's different that just being jailed for contempt.
Compelling someone to open a phone with a fingerprint is far from settled law. It should be litigated properly as part of the trial rather than with a "contempt" charge.
In this instance, it is the court that is attempting to end run an unsettled area of the law using "contempt".
A charge of contempt is still a charge.
You have the right to not divulge information from your mind that would incriminate yourself. In the US this is called the 5th amendment.
The alternative is that people have a right to stop the courts from functioning. Our interests in not having courts that can be easily thwarted probably does outweigh our interests in any single conviction.
It's only forever if you refuse to comply for that long. It is coercive. The justice system does not, because it cannot, ask you to comply. It forces you to comply and it does not take no for an answer or it would not function.
And holding a person is already a separate charge - kidnapping and unlawful imprisonment.
An actual sentence eventually has an end.
Self incrimination protections are there for a good reason. If the person is on trial, then they haven't pleaded guilty - they say they haven't done what they are accused of. If they are in fact innocent, if the court decided to enforce them into provide this information and jailed them for contempt, it would literally be indefinite because they are innocent and cannot provide information on what they don't know!
I guess that's why a key or fingerprint is allowed - it is definitely something that can be used one way or the other. If they key doesn't work, it doesn't work. Same with a fingerprint.
But a passcode - it is not definitive. The defendant may say they don't know it as someone changed it on them. They then type in a wrong code: how are you going to disprove that?