Yes, I do consider the child tax credit buying votes and I likewise consider farm subsidies vote buying as well. This situation, in particular, seems egregious because of the amount being proposed - $10,000 - and because the executive branch is planning to do it unilaterally. I would still disagree with the measure, but I wouldn't feel as strongly if this happened a result of a vote from Congress.
Politically speaking the best course of action for Biden is to say that the repayment pause will continue until Congress passes comprehensive legislation addressing higher education funding and reforms.
This would actually be better than $10K forgiveness, which is kind of a drop in the bucket for people who are really struggling with student loan debt, despite the previous commenter thinking the amount is "egregious".
