This is dealt with very comprehensively here
It introduces the topic as follows:
While there is no prohibition against work nor any forbidden labors, there is a wealth of halachic material concerning the issues. In the present article we will discuss the different elements of work and labor that involve some level of restriction on Purim. And while it is permitted to work, we will see that often it is not advisable
So, let's take a deep dive...
Megillah 5b relates how Rebbi planted a tree on Purim. Rav Yosef there questions how he could do such a thing if the day is established as a festival, to which the gemara concludes:
הֶסְפֵּדוְתַעֲנִיתקַבִּילוּעֲלַיְיהוּ, מְלָאכָהלָאקַבִּילוּעֲלַיְיהוּ
The Jewish people accepted upon themselves the prohibitions against eulogizing and fasting on Purim, but they did not accept upon themselves the prohibition against performing labor.
The Gemara also notes an anecdote with Rav who cursed a person for planting flax on Purim. From there, they conclude that it was the custom of the place to do so, and as such serves as an example where it is permitted but others have the custom to refrain from such action. Refer to Mishneh Torah, Hilchos Megillah 2:14 and SA OC 696:1.
Thus there is clearly a custom not to work. This view is brought in Orchos Chaim (Purim 27), Kol Bo and Rema 696:1. Yet this is also debated...
The Orchos Chaim goes so far as to write that because the custom against work has become ubiquitous, we excommunicate (cherem) anybody who works on Purim. This is also mentioned by the Aruch Hashulchan (696:2). However, other authorities write that working on Purim does not warrant so severe a punishment (see Kol Bo; Eliyah Rabba 696:1; Peri Megadim, M.Z. 1).
Moreover, the Birchei Yosef (696:2) writes that according to most Poskim it is not a universal custom, but rather depends on the specific location and its custom. The Rambam and Shulchan Aruch also do not note a universal custom, implying that the matter depends on local custom. These rulings imply that for Sefardim the matter of working on Purim is less severe than it is for Ashkenazim, who follow the ruling of the Rema.
Even if we assume that it is forbidden to work on Purim (based on the ubiquitous custom), the Peri Megadim writes that the prohibition does not apply on the night of Purim, but only during the day of Purim. This matter is disputed, and the Biur Halacha cites both opinions. Since the prohibition is only by force of custom, one can be lenient about work at night, even for those who are stringent to refrain from work by day.
The Magen Avraham (1) adds that even where the customary prohibition applies, it remains permitted to do things by means of a non-Jew. This is also ruled by the Mishnah Berurah (2).
Therefore, in summary work is allowed on Purim, but in some communities the custom is to refrain from labour, where it is forbidden. See the link in full for more details.