Answer

In principle, there is no cooking after cooking. However, the novel position of the Yere’im (brought in Rema, Orach Chayim 318:5) is that there is cooking after baking. According to his view, cooking can apply to a biscuit, because it is baked.
The Mishnah in chapter 3 of tractate Shabbat (42a) says that there is no cooking in a secondary vessel (with regard to spices and oil), and simply speaking this is not because it is an unusual manner of cooking or because of a change in the cooking process; rather, there is an assumption there that a secondary vessel does not cook (a problematic assumption, of course). See here:
https://etzion.org.il/he/%D7%A9%D7%99%D7%A2%D7%95%D7%A8-9-%D7%9E%D7%91%D7%A9%D7%9C-%D7%9B%D7%9C%D7%99-%D7%A9%D7%A0%D7%99
But the halakhic decisors wrote that for easily cooked items, cooking applies even in a secondary vessel (based on the Mishnah on 145b). Because of the uncertainty over what is considered an easily cooked item, the custom is to be stringent and not to cook even in a secondary vessel as well (again, following the Yere’im).
Now one must consider whether a biscuit is even cooked in liquid at all, even in a primary vessel. If it is, then one should be stringent even in a secondary vessel, because clearly the same thing happens to it there as well. Indeed, I am inclined to think that this is not cooking but only softening and heating, but when heating water it is explicit that this is called cooking, even though there too it is only heating.
Bottom line: there is definitely room to be stringent about this. To be safe, transfer it to a tertiary vessel.