Our freshman struggled more than they let on during their first semester. They can return to their school but haven't said definitively that they want to or are willing to put in the work. Any suggestions for how to navigate? I don't know if we want to pay for another chance if they aren't sure but don't want to send the message that we don't believe in them.
What does "haven't said definitely that they want to" go back mean? Ask your kid - you write as if you are afraid to talk to them.
If their grades are good enough for them to return, then they are probably not as bad as they may seem to you (see, for example, parent freaking out because their kid got an 89.55 grade, as if a B+ will ruin them).
My kid also struggled his first semester and didn't really pull things together until sophomore year - it was just dumb stuff related to his maturity level and ADHD. He had to drop a class here and there, had to retake one or two things, had iffy grades in a couple of gen ed classes. He made the deans list consistently after that first year, graduated with a 3.5 and is in grad school with straight As. Again, talk to your kid to find out what's really going on.