As I understand Filoni's words, there is a little bit of the old Anakin reaching out, but it's basically immediately crushed by Vader. It's perhaps worth noting that this isn't wholly unprecedented for Vader; although it doesn't cause Anakin to resurface in any real sense, a flood of memories causes Vader to temporarily lose control in the canon novel Lords of the Sith, set about ten years earlier:
He'd floated alone in an escape pod over Ryloth once, spinning high over its surface, after crashing a cruiser into a droid control ship. Another name bobbed up and broke the surface of the sea of memory.
Ahsoka.
He'd called her "Snips" sometimes.
[...]
Ryloth filled the viewport as the ship descended. Seeing the mottled browns of its surface, the smears of green and tan, dredged memories of other times up from the sludge of his distant past, names he rarely thought of anymore. Anakin. Mace. Plo Koon...
[...]
Flames from the friction of atmospheric entry sheathed the ship. Fire surrounded them. Fire.
Mustafar.
Obi-Wan.
He used his ever-present anger to burn away the memories, but the charred husks of the past clung to the forefront of his consciousness.
Padmé.
He rarely allowed himself to think her name.
His rage slipped his control and he squeezed the control stick so hard it cracked. His breath came hard, fast, loud.
Lords of the Sith Chapter 10
The question of what happened to Ahsoka is answered (as much as is possible) herehere. However, I will at least confirm that the figure we see walking back into the Temple is not the Convor; it's clearly humanoid:
However, it's not clearAlthough many fans speculate that it's Ahsoka; when I squint, I can kind of see horns on the figure, consistent with Ahsoka's horns, but we don't know; Filoni is coy on the detailsAhsoka, as you'd expect:this has not yet been confirmed.
IGN: Let's start with the ending. I'll just go there… Ahsoka's totally alive, right?! That's her walking away in the cave?
Filoni: Is that what you saw? That's so interesting. That's so good. You know I think it says a lot about who you are, which is great. You're an optimist, and I think that that's strong, I think that that's strong. [Laughs] It's an interpretation.