Tevilas Ezra has nothing to do with Bias Shemesh. The Tuma is De’oraysa and lasts until Bias Shemesh. Ezra’s Takanah is besides that.
Although the strict Halachah seems to do away with the Takanah, many Geonim, Rishonim and some Acharonim have not taken it that way. The Shaalos Tshuvos Min Hashamayim even criticised the Yerushalmi on this.
Regardless of the Chiyuv or otherwise, it is widely considered a prerequisite to learning Toras Nistar.