So I'm landlocked at home while I wait for a parcel to arrive, and I have nothing better to do than think about the most recent episode of Doctor Who. It's a dirty job, but I'm up for it!
I'd say upon a rewatch my first impression still stands — this episode being a sequel to "Midnight" is tenuous at best. But since it's spelled out in dialogue that this is the same planet and entity, let me one-up that a bit.
1. "The well" is a double sequel.
Between my first and second watches of this one, I went back and rewatched "Midnight", but also "Listen". I still think there are more elements from the latter in "The well":
CLARA: You know, sometimes we think there's something behind us. And the space under your bed is what's behind you at night. Simple as that. There's nothing to be afraid of.
(The bed creaks as someone sits on it. It sags to within inches of Clara's nose. Rupert starts breathing quickly.)
CLARA: (sotto) Who else is in this room?
RUPERT: (sotto) Nobody.
That's not a cut and dried connection, but the whole scene with whatever it is behind them in Rupert's bedroom just has more resonance with this recent episode's entity than the parroting one possessing Skye in "Midnight". So, I'll meet you halfway and propose that "The well" is also a cheeky, unofficial sequel-of-sorts to "Listen".
2. Shaya is a Doctor stand-in:
I ran as a child. I ran from the wildlands. I ran from those monsters and never looked back. And I ran across the galaxy, with one aim. To do my duty. To help. To protect. To bring hope.
That pretty much sums up the Doctor too, right? At the very least their MO when companions or other bystanders are concerned — running, and hope. "Hey, we ran, you and me. Didn't we run, Lorna?"
episode spoiler
So Shaya sacrifices herself quite literally in place of the Doctor, where they couldn't do the same without leaving Belinda stranded. This very literal reference to the Doctor's worldview could be foreshadowing of a situation in the finale where they have to make a similar decision.
But what are the "monsters" Shaya talks about? Do they have to do with the implied devastation of Earth, or is it just going to be a given without further elaboration that there will always be monsters out to get human-like civilisations?
I'm hoping this will come to bear on the finale as well.
3. There is a real deep genre reference to all of the episode:

I didn't think of this myself, Bleeding Cool's writer did:
"The Well" is virtually a remake of the 1965 Italian-US-Spanish space horror movie Planet of the Vampires, directed by Mario Bava.
By '65 I'm fairly certain Doctor Who had already broken in the "base under siege" formula, but Planet of the Vampires is widely acknowledged to have inspired a more modern milestone in scifi/horror — Alien.
It also has the basic premise of a space crew landing on a barren planet to investigate the disappearence of the last people to go there. Oh, and invisible monsters. Besides, PotV is a pretty cool, atmospheric movie in its own right. Very recommended for the cinematography alone.
Bleeding Cool thinks that
the biggest visual homage and clue that the makers of "The Well" have seen Planet of the Vampires is the dark blue skintight astronaut suits they wore in the episode
but to be honest I think Bryan Singer's X-men has more of that design DNA... But wait! There was also:
4. That time the Doctor found a derelict spaceship and met actual vampires
In "State of decay" (1980) the fourth Doctor and Romana investigated a medieval castle that turned out to actually be a downed spacecraft, and buried deep beneath — not in a well, but down several stairwells as I recall — lay the king of the Great Vampires. So with a bit of finagling we might even tie a 45 years old story into the package and declare the "Midnight"/"Listen" entity one of the Great Vampires, ancient enemy of the Time Lords.
Well(!), I think I theorised that into the ground, and my parcel still hasn't arrived! Thanks for reading, I'll probably have to do some real work now.