The Borderlands series keeps bouncing around what exactly it looks like when a psion communicates with you telepathically. In the first game, it didn’t even seem like it was supposed to be telepathy, more like Angel (a psion who also has access to some amount of techno-gadgetry and uses the latter to pretend she’s an AI) has hacked into your space phone. Although Angel does first contact you before you get your space phone, but that’s the same scene where she tells you to get off the bus while it’s still in motion, so I’d chalked that up to another writing oversight – Angel’s lines seem to be written and delivered with only a very vague idea of what part of the game they’re going in. But then in Borderlands 2 they retcon that dialogue mistake by having Angel deliver a line word-for-word under Handsome Jack’s instructions, and Jack can’t see what the player is up to.
By Borderlands 3 it’s unambiguous that the effect used is supposed to indicate psion telepathy, because friendly telepath Lilith uses it without access to any of the techno-gadgetry that Angel was using in the first and second games.
Here’s what Angel’s telepathy looks like in the original Borderlands 1:

It’s an artifact of the more photorealistic original version of the game, and at some point they replaced it with a very AI-looking thing for Borderlands 2. When they updated Borderlands 1, they backported the Borderlands 2 Angel into Borderlands 1.

Except I think that Borderlands 2 might’ve had the original photorealistic style Angel at some point? I never played that version of the game, but I came to Borderlands 2 several years after release. Later in Borderlands 2, Lilith gets captured by the villain that Angel was working for and plugged into the psychic-juicer that Angel used to powering. During this part of the plot, Lilith communicates with you using a dot-matrix-y looking thing just like Angel’s there, one which I cannot for the life of me find a screenshot of, but it’s basically the same as the second picture of Angel, except it’s Lilith’s face instead of Angel’s and also orange.
But while researching this post, I found live action footage on YouTube that’s tagged as being for Borderlands 2. It looks like the live action clips they would’ve made footage out of for Borderlands 1-style telepathic communication, and from the body language, it does look like it was for Borderlands 2, because Lilith is breathing heavily and looks all freaked out, as though she’s just been kidnapped by a megalomaniac who’s torturing her. The telepathic face thing doesn’t actually move their lips in sync with the message being communicated, which means live action Lilith there has no actual lines for me to double check, but this checks out that at some point, possibly even when the game released, there was a live action Lilith for her telepathic messages near the end.
They definitely have this in Borderlands 3:

God this looks terrible. For starters, Lilith is a playable character in Borderlands 1 and a major NPC in the Pre-Sequel and especially Borderlands 2. We’re very familiar with her appearance, and she looks like this:

Not only does the live action version look like a cosplayer, that expression doesn’t match Lilith’s attitude either in general or in that specific conversation at all. What it matches is the cooing-mother schtick that Angel had in Borderlands 1 and the first half of Borderlands 2. Lilith’s neither written nor voice acted like she’s adopted that mannerism. Her attitude is pretty muted and low-key, not part of the comedy mayhem but unfazed by it. As is often the case with these sorts of things, leadership figures play the straight man while the followers get most of the punchlines, it’s common because it works. But then Lilith has this bright beaming smile while greeting a vault hunter she’s never met before and who is only loosely allied with the Crimson Raiders (you share an enemy, but at this point in the plot, that’s it).
The live action psionic communication thing was always super out of place once Borderlands pivoted from its pre-release photorealistic style to its series-defining cel-shaded comic book look, and it makes plenty of sense that they pivoted away from it, even redoing Angel in the new style for the Borderlands 1 GOTY edition. But then they went back to the weird live action thing for Borderlands 3, and they didn’t even get the facial expressions to match up at all with Lilith’s in-game character model or the delivery of her voice lines. I think they wanted Lilith to be as reminiscent of Angel as possible, because the whole opening is a recreation of Borderlands 1’s opening? Borderlands 3 came out after a five-year lull in the mainline series (and that’s counting the Pre-Sequel as a mainline game) and more than a decade after the release of the first game, so I guess they were aiming for nostalgia. But while I thought the recreation of the first game’s opening was kind of neat (and they abandon it before it becomes repetitive), they didn’t need to have Lilith be aping Angel’s exact facial expressions for that. Let Lilith be Lilith.