No, that is not weird. You should just use the time wisely. First, use the health insurance as much as you can: if you have an option of a mail order pharmacy for three months rather than a local pharmacy for one month, use it. If there is anyone at all at your workplace who has been happy with your work, ask them to write a LinkedIn endorsement - would not hurt in your subsequent job search. If there is no one, that is OK, too. Your being relieved evidences that this job is not the right place for you, period.

The management is not performing well by being vague about what you need to do to stay. The management has to come up with attainable, measurable goals and clear criteria of success/failure. But you cannot make them do so because they are already going "above and beyond" by putting you on probation: the employment is at will. So they can get away with a lot.

I am sorry you have to go through it but I trust that in the end you will find a better place for yourself.