Read the baggage policy
Amtrak Cascades - Baggage.
I don't see anything saying that you can't put a folding bike (unfolded to its full size) into one of the reserved bike storage rack spaces. (On the non-Cascades train I rode, the bikes hang from a hook on their front wheel and you are required to bring a strap to secure it and a lock to lock it up to the rack if you wish.) Nor do I see anything saying that if you bring a walk-on bike and store it in the bike rack space you've reserved for a fee, that it would count as 1 of the carry-on items you're allowed, so I assume you can still bring the 2 items of luggage plus the bike if you reserve a bike space. If you take the folding bike in its folded condition on board as carry-on baggage, it counts as one of the 2 allowed carry-ons. Certain small items that you can also bring on board are exempt for the carry-on limit.