If Biden announces he is forgiving $10,000 of student loans, am I owed
money? It certainly seems fair that I should receive a check in the
mail for $10,000.
No. "It certainly seems fair" is not the measure by which laws are deemed valid or not.
Is there any legal recourse to this announcement?
If a $10,000 forgiveness is announced, is there a basis for a class
action lawsuit against the Federal Government?
Someone receiving a benefit from the government is not a legally cognizable harm to you.
Even if the law or order was blatantly illegal, you and people similarly situated to you would lack standing to bring a lawsuit challenging such a federal government action simply because you were similarly situated at some time in the past and did not benefit from the law or ruling that did not yet exist at that time.
Laws and executive orders are not retroactive unless they say so, and are not required by law to be retroactive in effect. Indeed, sometimes laws with retroactive effect, called "ex post facto" laws are unconstitutional.