On average, how long do sessions tend to last in Adventurers League organized play for D&D 5e?
Average is difficult to pin down.
There's no good way to determine how long the "average" session is, because there's a great variety of content available. That said, the DDAL Content Catalog can provide some guidance on expected lengths. You could calculate an average based on all published content, but it wouldn't reflect popularity. Some content is simply better than other content, and as a consequence played and replayed more often.
Modules range anywhere from five one-hour mini-modules, to two-hour, four-hour, and a small number of eight-hour modules. Season 8 added the concept of one-hour "bonus objectives" to both two-hour and four-hour modules, resulting in the possibility of any single module taking from one to eight hours.
I've been running and playing DDAL for many years now in game stores, at home, and at conventions. Over that time, I've come to the conclusion that the published module length is generally off by about 50% if you want to give the full, unrushed experience: two-hour modules take three, four-hour modules take six, and so on.
This is problematic in a game store or convention where the time is limited. You either have to split up the module (and hope you get all the same players for the second part), cut down the module to squeeze it into the allotted time (giving an inferior experience), or drastically curtail roleplaying and characterization (no fun in my book).
Hardcover adventures can take many, many hours - sometimes over a hundred (I recently completed playing Dungeon of the Mad Mage over 36 sessions at four hours each). While they can be done in a game store with a rotating cast, they're best done with a fixed cast - trying to rush or squeeze a hardcover adventure is highly detrimental to the storytelling.
Most sessions are specifically timed to last about 2 hours (exception is longer sessions, typically scheduled on weekends, that tend to last about 4 hours). Some campaigns and modules are too long to fit in this time frame, in which case they would be broken up into multiple parts so each part can be completed in about two hours.
How long the session actually takes depends a lot on the speed of the DM and players, so it can vary a lot, but generally the modules are written with the idea that they can be completed in a 2-hour time frame.