We know that saying brachos in a bathroom is Assur. Would the same halacha apply regarding saying them near a bathroom with the door open ?
this doesn't seem to answer the question ?!
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There are two issues here. One is whether our bathrooms have the status of the beit hakisei of the traditional halacha, the second whether we can say a bracha close to a beit hakisei.
Whether our bathroom have the status of a beit hakisei is a machloket poskim. R Yirmiyohu Kaganoff for instance writes
The later-day poskim dispute whether our bathrooms have the halachic status of the beis hakisei of the days of Chazal. Some poskim are lenient since our bathrooms are much cleaner than old-time outhouses (Shu’t Zakan Aharon 1:1; Shu’t Minchas Yitzchok 1:60).
Others contend that our bathrooms should still be treated as a beis hakisei (Shu’t Yechaveh Daas 3:1). Both the Chazon Ish (Orach Chayim 17:4) and Rav Moshe Feinstein (Shu’t Igros Moshe, Even HaEzer 1:114) rule that we should treat our bathrooms as a safek (questionable) beis hakisei.
The universal practice is to not recite brachos in the bathroom, but some people are lenient to wash their hands there. Rav Moshe rules that one may not wash for bread in our bathrooms, but one may wash his hands there before davening, although one should dry one’s hands outside the bathroom.
From this R Kaganoff concludes that one should not recite a bracha [...] facing the bathroom when its door is ajar. However, if we assume that it is only questionable, then one may have grounds to be lenient.
R Moshe Feinstein does indeed provide such a leniency. He writes (Even Haezer 1:114) that since the walls of our bathrooms are also an integral part of the house, we can ascribe the same status to the door doorframe as to the walls and consider them to be part of the structure of the house and not part of the bathroom. Therefore he rules that [...] one may recite a bracha opposite and outside a bathroom even when the door is open (even if tzo'ah is present in the bathroom as it is considered as in a different domain). R Tzvi Pesach Frank reaches a similar conclusion (Har Tzvi OC 1:48). R Moshe Feinstein further discusses how synagogues should be built to avoid the issue.