"... ICE you still have the rights to an attorney and you have legal rights to claim ..."
Which is exactly what your example Rumeysa Oztruk is doing, and ICE seems to be respecting the order. Which undercuts your point number 4 a bit. If she asked to leave detention by leaving the US, would ICE stop her, and forcibly keep her in detention? I'm going to assume "no" ... why would ICE violate one inconvenient law, but respect another?
ICE could make the argument she is only in detention because she explicitly asked for it, that she is only detained because she delayed her deportation.
But more than that, I think Rumeysa Ozturk is yet another example of someone who just won't get support from people. She's a rich kid being given an easy path in life, yelling loudly how bad the people helping her are, and ... good luck defending that one in an economy where people are losing jobs.
Probably she's here on the dime of her parents, with a scholarship (a PhD IS a scholarship, a subsidy, so there's really just a question of how much it covers), with the goal of letting her immigrate into the US and get a better job, better life, here than she could ever hope to get in Turkey ... the world is extremely UNfair, and she is the benefactor of enormous unfairness.
Given what has happened to the economy in the past few years, and how many people have experienced setbacks 10x worse than losing a free and easy path in life.
To some extent people don't seem to realize "you want the right for an easy path in life for people in X (Turkey, China, Gaza, ...). Fine, Great even, but the US government FIRST must create such path for everyone in Appalachia. You want it done for Turks? Great. I even agree that that should be done. But not by the US government, by the Turkish government"
And yes this is a "if I can't have it, you can't have it either" argument, and it is mean, jealous and vindictive ... but Rumeysa's defense is essentially "let them eat cake". She has support from the US government for her education, which many locals don't have (and many MAGA are going to say a student in education sciences isn't helping the US, she's just taking jobs and subsidies away from US people. This isn't entirely untrue. She is not an exceptional talent that will elevate the US, economically or politically, or even in sport, or otherwise. In other words, she's "wasting" the US government support she's receiving, bluntly why shouldn't US citizens have first dibs on wasting US government support?)
In that situation she goes out writing op-ed, complaining, doing what the executive (even under Biden) would consider sabotaging US government policy? sigh. Really?
To add insult to injury, to put it VERY mildly, what is happening in Turkey, is still a lot worse than what is happening to her. The US doesn't seem to be able to count on Turkey's help to rectify those problems. She wants to fix the world, yell at a government? Then go join the yelling at Turkey's government, they have destroyed their universities, replacing all teachers with Erdogan loyalists, imprisoning tens of thousands just for holding a university job (and I guarantee every last teacher, assistant and student on a visa was deported from Turkey, regardless of their political stance). Turks, who supported that (she seems to care about religion, which in Turks is a near-guarantee that they support Erdogan). And then she loudly criticizes the US for using money and visa policy to influence university positions? (as opposed to what HER government does: arresting, imprisoning for decades, even torturing the entire faculty staff)
So I also predict you will not see any real uprising against this until people can't make the argument "she could easily have avoided this in 10 different ways and effectively chose this path".
It sucks, but you just won't.