let's start off by briefly establishing the relationship between these two (or more appropriately one lack thereof): the grand inquisitor is implied, and confirmed by word-of-god, to be one of the temple guards present during the temple bombing trial, an event which aided in his descent to the dark side. barriss's speech spoke to doubts he already harbored about the order, and her own criticisms of the order confirmed a very particular bias of his about the jedi, one antithetical to the intention of barriss's speech which spoke to a collective disregard for the tenants of jedi order, namely that "fighting for dark-side" had warped the core of their belief system. we've been shown that every one of the grand inquisitor's choices has been made in selfishness, not selflessness. his many resentments and grievances are rooted in personal dissatisfaction and inadequacy with himself, that the jedi order did not balm his hurt is what led to his ultimate repudiation of it. barriss's resentments and grievances are rooted in a deep love for the jedi order that raised, loved, and respected her. they both felt betrayed by the order's misrepresentation of itself, but the grand inquisitor wrongly attributed barriss's feelings of betrayal to his.
now with that groundwork laid, let's talk about the threads! working top-down: the moment barriss defeats dante, her inquisitor helmet is presented to her. it was forged for her before she landed the killing blow. she had no say in its creation. the grand inquisitor is this coven's proud leader; he is responsible for his flock and fortress, and he chose this for her.
a replica, a replicated lapse in self-indulgence, a moment in time where barriss lets her darker impulses, her anger and her hatred, have their say. its design is slightly adjusted to better fit barriss and the inquisitorius' aesthetic, and in there is the implication she is wanted by this empire, she is an asset to this same regime she warned the republic of. we know she regrets the acts of violence she committed under duress as evidenced by both the remorseful expression she shoots ahsoka and by this deleted scene where she explicitly apologizes to her. but the grand inquisitor does not want her moving past this moment. it's a deep well of emotional turmoil that the dark side is eager to drink from. he wants her stewing in it, and 'it' taking the shape of a mode of sensory deprivation is a very happy coincidence! the dark side is at once a state of stasis and parasitism; it successfully feeds off of isolation and hyperfixation, oftentimes from a particularly traumatic event. barriss is forced to become the face of the darkest, most regrettable moment in her life, one where she becomes the betrayer. it reopens wounds which remind her she can operate as both aggressor and aggrieved. it strips her of a voice, modifies her speech, while also working as effective blinkers (blinders/tacks like those used on animals to limit their discernment). the former perpetually-masked temple guard is well acquainted with this hell and assuming the role of traitor! we'll get into his projection in a moment.
after barriss is given her 'gift', we hard cut to her now in full regalia. it's very in medias res; she seems to be in conversation with the grand inquisitor before the rest of the inquisitorius' fledgling brothers and sisters enter the scene. whatever might have been said is left up to our imagination, but judging by both of their expressions, i imagine it was a threat veiled in niceties, much like her 'gift'.
to understand how the grand inquisitor implements fashion mirroring (projection by any other name!) here, you should first have a keen familiarity with the visual language of the inquisitorius' aesthetic sensibilities so to properly pick apart what differentiates barriss's uniform from the rest of the herd's. unifying elements of inquisitors' uniforms are the use of black, grays, and reds, as well as a liberal application of plate-adjacent armour, and some ribbing which likely allows for better mobility.
here we have mommy dearest doing his capital best to suit up his mini-she. most notable are the silhouette's pauldrons and the piece of armour that is something between chest plate and gorget (his gorget has been readapted to be more pronounced/realistic since its inception in rebels and appearance in owk). minor details like the boots and imitation vambraces are also of note, but what i prefer to focus on is the how and why. there is a deliberate likeness, but it's as if hers had its edges sanded down. making her appear less threatening invites predation. it's not enough that she has proven herself capable of murdering her competition, she must remain in a state of hypervigilance around her brothers and sisters. this parasite has a varied palate! fear is a nice little amouse-bouche to rage. the grand inquisitor wants her skills in the dark-side ever-honed and improved upon if she's to be a testament to not just his teachings, but him. see, barriss does not exist to him as a person. since the trial, she has existed conceptually and amorphously to him as an extension of himself and his own issues with the order, but they do not share the same sentiments regarding the order's issues. their dynamic, in truth, more closely resembles that of a narcissistic parent and their child. the child apprentice exists simultaneously to placate his wounded ego, and to fill a void left by (self-imposed) loneliness. i find it a very appropriate representation of this brand of narcissism, to have their authentic relationship be expressed through the medium of costume; it's external, but rarely superficial, it's an assignment, and it's imposed, but unveils so much about both characters' true natures.
