Okay, this one is a trivial issue but it occurred to me yesterday (I was making a long drive).
Why does Yelena Belova have a Russian accent? We saw in previous movies that she was raised in the United States from an early age and even believed she was an American. She spoke English with an American accent.
So when did she pick up a Russian accent? If anything, it would make more sense that she speaks Russian with an American accent rather than English with a Russian accent. And you’d think that during all of that spy training she endured, they would have made sure she kept her original accent and could pass as an American when needed.
My guess is that the Russian accent is more threatening. It just sounds better.
It doesn’t bother me nearly as much as Scarlet Witch’s accent that vanished after Age of Ultron.
My headcanon is that she adopted it intentionally later in life to fit into Russian life, and has been doing it so long that it became her natural accent. Because in the MCU, Russians speak Emglish with a Russian accent more often then they speak Russian. 
Or, it was forced onto her as part of her Black Widow training, and she felt no need to unlearn it.
There is no reason this should bother you. Her accent comes back when she is angry or emotional. As someone who is bilingual I noticed it instantly and it is perfectly acted, not a mistake.
Some younger hero needs to confront her about it and accuse her of being a poser, much like she accused Natasha of being a poser for using the three-point ‘hero’ landing. (And then Yelena started doing that landing herself…)
As a digression I’ve always rather liked that acting technique when done well. There is a tiny moment in the film Topsy-Turvy where I think it is Kevin McKidd who is playing a stage actor happily chatting with other actors in a dressing room, all using archly posh accents. Something happens to agitate him and his accent starts slightly shifting to a lower-class one as he starts getting more upset. His background is never described, it is never remarked on and he is just a character actor with a tiny part in the overall film. But it immediately made me pay attention to this tiny little throwaway moment and increase the verisimilitude of the scene.
I never noticed her accent coming back though.
In WandaVision in particular I am pretty sure she never speaks with an accent despite being very distraught at multiple points of the series.
Oh no. It definitely comes back when Geraldine / Monica asks her about her brother. She has a rather thick eastern European accent just before she blasts Monica out of the Hex.
Also when she confronts the agents of SWORD later on.