Is there a term for a sentence that suggests a question but isn't one?

I believe the term you're looking for is indirect question.

a question that is reported to other people in speech or writing, rather than the exact words of the original question, for example 'He asked me what was wrong.' (Cambridge Dictionary)

Various ESL sites specifically cite the "I wonder..." case as an example of an indirect question.

Example:

Direct question: Where have they been?

Indirect question: I wonder where they have been?

Notably, that example does use the question mark at the end. It is not always considered incorrect; it really depends on whether you want it to be perceived as a question or a statement. For more info about that, see this related question and its answers.