What, if any, is the official, written, Adventurers League guidance on the harvesting, purchase and/or use of poisons? As a budding assassin, it would help me a lot to understand what is permitted in AL.
The basic poison found in the PHB can be bought, created, and used like any other mundane item. The Adventurer's League Player's Guide allows you to use almost all PHB rules.
D&D Player’s Handbook™ (all rules except rolling ability scores and hit points, some alignment restrictions)
The Adventurer's League FAQ specifies that you can only use DMG material (including poisons) if it is explicitly obtainable in a campaign. The full entry contains several irrelevant points, so I've excerpted the bit you care about.
Can characters use any material from the Dungeon Master's Guide, such as poisons?
As a rule, the Dungeon Master's Guide is not a valid character resource for the Elemental Evil storyline season. Since the Dungeon Master's Guide is not a generally valid character resource, characters cannot use any material from it other than magic item descriptions without campaign documentation giving them access.