Q: If someone does melakhah while making preparations for the weekday after tzeis, but before they have said havdalah, does this violate the rule against preparing on Shabbos for a weekday since it’s still technically Shabbos?
A: Preparations for the weekday made after the time of Tzet HaKokhavim (“the appearance of three stars”) on Motza’ei Shabbat does not fall under the prohibition of making preparations on Shabbat for the weekday since it is no longer Shabbat, but the first day of the week. There is no such thing as “technically Shabbos” (as some like to call any time after the end of Shabbat but before havdalah is recited) since it is either before or after Tzet HaKokhavim – which is itself the deciding factor in determining which day it is and NOT the havdalah service. Therefore, if it is before tzet then it is for sure Shabbat, and if it is after tzet then it is for sure no longer Shabbat.
However, it is assur le-khatehilah mi-de-rabbanan to do melakhah before one has said havdalah either during the Aravit prayer or on a kos (i.e. recites havdalah over a cup).
So, to directly answer the question: Yes, there is a problem with doing melakhah (or presumably making preparations for the following day) before one recites havdalah. It is not, however, a problem because of the prohibition of preparing on Shabbat for a weekday since it is no longer Shabbat, but falls under the general rabbinic prohibition of resuming melakhah before the havdalah is recited.
However, if you have already recited “Barukh...ha-Mavdil ben kodesh le-hol” in your Aravit prayer, then you are allowed to do melakhah, as long as you do not eat or drink (with the exception of water) until you also recite havdalah on a kos.
See: Rambam, Mishneh Torah, Hilkhot Shabbat 29:5-7; Arokh HaShulhan OH 299:19