I’ve been thinking about this for ages, and I figure you might have some thoughts about it so: what even IS an Overseer? Are they just lords? Are they a separate thing? It bothers me

So, to understand the context on this, you need to know that the writers—for at least some portion of the plot—didn’t think “apprentice” was a rank. You have a master, and you’re their apprentice, but you’re a full Sith the moment you pass your trials; lords are just more important Sith.

Sith Titles - SWTOR Codex

The Sith Order bestows a number of titles upon its followers, as befits their rank and power. These are the most common:

Acolyte: A Sith acolyte has not yet completed his or her trials in the Sith Academy, and may well die before becoming truly 'Sith.'

Sith: An acolyte who completes the trials and is accepted as the apprentice of a Sith Lord is considered Sith--no more, no less. Any non-Sith, however, is expected to refer to a Sith as 'my lord' out of respect.

Overseer: An instructor at the Sith Academy is called an overseer. Overseers are often Sith Lords, but that rank is not a requirement; they may simply be Sith with a talent for instruction.

Sith Lord: A Sith who advances in the order's hierarchy will eventually be elevated to Sith Lord. His or her name is preceded by 'Lord' in formal address. In the modern Empire, 'Dark Lord' is synonymous with this term.

Darth: The strongest Sith Lords ascend to the position of Darth. Many take a new name at this point, symbolically embracing their transformation into something greater.

Emperor: There has been only one Sith Emperor since the Great Hyperspace War over 1,300 years ago. He is supreme.

This is, obviously, incomprehensible nonsense. Even the writers themselves thought so, since in most cases they very clearly do treat “apprentice” as a rank, and “Dark Lord” is almost never used for anyone but a Darth except in Korriban dialogue. The weird inconsistencies in how Sith ranks work are mostly centered around Korriban—they show up in the dialogue, a bit, and in a Korriban lore object. And the way the overseers are written is based on that half-deprecated lore: they’re Sith, and they’re not apprentices because they don’t have masters, but many/most of them aren’t lords.

In a version of the Empire where the worldbuilding is a bit more consistent… we’re told that only Sith are allowed within Academy walls (barring orders from on high), and shown that sometimes failed acolytes are sent to work in Academy infrastructure (Klemral, if the warrior takes a light side option, even if he doesn’t stay there). It’s likely that most overseers are drawn from the ranks of acolytes that have enough skill to make good teachers, but don’t have the power to make it as true Sith. A few of the others are former apprentices or lords who were disgraced, and are serving the Order in their punishment. The remainder are lords in the Sphere of Sith Philosophy who simply treat their job title as taking precedence while on the job—as the blue-robed Inquisitors do. Inquisitor Zyn is probably a lord too, but you wouldn’t call him “Lord Zyn” unless you met him at a gala.