No, Blizzard did not ban multiboxing
What did they do, then?
Blizzard banned the use of third-party input broadcasting software in World of Warcraft. This software was used to broadcast keystrokes to multiple game clients at a time.
What is input broadcasting?
Input broadcasting is when a program takes keystrokes and sends them to multiple game clients.
So, multiboxing is still allowed?
"We’ve examined the use of third-party input broadcasting software, which allows a single keystroke or action to be automatically mirrored to multiple game clients, and we've seen an increasingly negative impact to the game as this software is used to support botting and automated gameplay. The use of input broadcasting software that mirrors keystrokes to multiple WoW game clients will soon be considered an actionable offense."
Policy Update for Input Broadcasting Software, November 3, 2020
"Multiboxing, or playing multiple World of Warcraft accounts at once, is not a violation of our End User License Agreement. Please note, however, that use of input broadcasting software may result in account penalties."
Is multiboxing the same as botting?
No. Botting is when a program plays the game for you without you having to do anything.
When a player multiboxes, they simply run and play more than one copy of the game at a time.
Is multiboxing automated gameplay?
No. Automated gameplay is the use of software that runs outside of the game that makes decisions and performs actions for you.
Consider fishing in World of Warcraft. You cast your reel using the Fishing ability, wait for a fish to bite, then click the lure to retrieve your fish. Using automation software, it's possible to automate parts of the fishing process such as automatically clicking the bobber with the cursor when a fish bites. As this is not possible to do within the game, it is considered automation and is against the Terms of Service.
Multiboxing software, however, does not automate any part of gameplay beyond what is possible in-game. Players are still responsible for making decisions and performing actions themselves.
Are multiboxing addons or in-game macros considered botting or automated gameplay?
No. Generally speaking, it is not possible to automate gameplay with in-game macros or addons. This also applies to popular addons like Weak Auras. There are technical limitations within the game that prevent actions Blizzard considers botting or automation. Casting spells in combat, for example, requires user input such as a mouse click or keyboard key press. It is not possible for an addon or Weak Aura to cast a spell while in combat. Additionally, it is not possible for a macro to have conditional logic beyond a very limited set the game allows. You cannot create an in-game macro that automatically targets a healer and casts an interrupt, for example.
Multiboxing addons offer additional utility such as inviting characters and following/unfollowing. As these are all possible to do within the game, they are allowed by Blizzard. There are limitations to following, such as being disabled in pvp. This includes Warmode pvp combat, battlegrounds, and arenas. This restriction is not an addon or macro one; the feature itself is disabled in certain conditions.
Macros that exist outside of the game, such as macros made in keyboard software, can potentially be against the rules. Blizzard's guidance on creating macros outside of World of Warcraft is to make sure you don't do anything that you cannot already do with in-game macros.
Is all input broadcasting banned?
This is a question Blizzard has been asked a few times without a direct response.
Technically, the definition of input broadcasting is pretty broad. Certain types of mice and keyboards use input broadcasting. Applications like the on-screen keyboard and specialized software and peripherals for physically challenged players also use input broadcasting. These are still allowed by Blizzard and there are no known cases of a player being banned for using any of these things.
It appears what Blizzard means by input broadcasting is input broadcasting to multiple game clients concurrently. By disallowing concurrent input broadcasting, it becomes a lot easier for Blizzard's anti-cheat software Warden to detect abuse.
Note: some mice and keyboards have the ability of creating macros that allow you to do things not allowed by Blizzard such as perform more than one keypress at a time. These macros are against the Terms of Service and may be actionable by Blizzard. Blizzard's general guidance in this case is to avoid making macros that cannot be done with in-game macros.