Beidou build recommendations
Regarding Weapon Choices
Serpent Spine is a fine choice for sub-DPS Beidou and can outperform Wolf's Gravestone by a significant margin when Bennett/Sara ATK buffs are applied. Be sure to use Beidou in slot 1 to pre-stack Serpent Spine before starting an abyss floor.
Depending on the amount of ATK% buffs you're getting, this weapon can overtake Wolf's Gravestone in personal damage.
Assuming 260 team energy, Akuoumaru outperforms Skyward Pride on a low ER requirement Beidou (where she is paired with other Electro characters to battery her energy needs). At [R3+], it becomes exponentially better and comes very close to Serpent Spine and Wolf's Gravestone.
Regarding Artifact Sets
Even after considering the 4-piece set effect, you should refrain from investing into Energy Recharge beyond what is needed to burst off cooldown as it will result in a damage loss as compared to prioritising offensive stats such as ATK/Crit. In team comps where Beidou has low ER requirements (i.e. when paired with electro batteries), a Noblesse Oblige (2) / Thundering Fury (2) / +18% ATK set (2) [Choose Two] will outperform Emblem of Severed Fate (4).
This set works best in an Electro-Charged or mono Electro comps.
This set could be considered if the team doesn't have a Noblesse Oblige (4) user, do note that sometimes Beidou doesn't benefit from the ATK buff from the 4 piece set if she's the set holder, so Beidou as a Noblesse Oblige (4) holder isn't really recommended.
Artifact stats priority
crit rate, crit dmg atk% er em atk