The Pact of the Tome states that the Warlock can choose three cantrips from any class's spell list, but Thorn Whip does not appear. I'm pretty sure it was there in previous versions, and I do have access to the Player's Handbook (so it's not a question of not having the spell available to me at all, just not in the drop-down lists for Pact of the Tome). Am I missing something, or is this a bug?

It shows up for me. If you only have access to the PHB via content sharing, make sure this character is in that campaign. If you purchased a license for the PHB on this site yourself, check that your entitlements are in sync.

Having a similar issue myself at the moment. Created a campaign to store some extra characters in. So at the moment I'm not technically the owner of the character (it belongs to a sock-account) but I am the DM of a campaign I put it in. I was able to add other PHB stuff I own on this account but not the sock-account. (Drow race; Great Old One subclass) So in general, I'm able to use DM privileges of editing the other account's character while using stuff I bought on this one.

For checking the entitlements, where would I look for that? And @DrakkynDeth did that work for you or did you find another solution? (Worst case I just homebrew copy Thorn Whip since my homebrew is showing up in the character creator.)

EDIT: Did a quick check. Thorn Whip showed up as a Pact of the Tome cantrip option for another Warlock that belongs to this account. So it's just the campaign-character that's having issues to my knowledge.

Quote from VitusW >>

For checking the entitlements, where would I look for that?

 
Here: (https://www.dndbeyond.com/account/marketplace).

Thanks, Sposta.

Under there I saw the message "Your entitlements data is in sync! You should have nothing to worry about, but contact our Support Team if you're having problems accessing your purchased content." So I should be good. (Player's Handbook was under the current product licenses.)

So would this then just be possibly an issue with trying to a modify a character this account doesn't own? (Wondering if DM position has any limits on what it can add to a character in a campaign it has.)

Is content sharing active for that account? If not, that’s your problem. If it is, try turning it off and back on again.

Quote from IamSposta >>

Is content sharing active for that account? If not, that’s your problem. If it is, try turning it off and back on again.

 I don't have content sharing. (No subs.) I was going based on being able to use this account as the DM to edit the character for the other. For the most part I can add stuff from the PHB (this account owns) that the other account does not. (Race, Subclass, even other PHB spells.) Hence my perplexion with Thorn Whip seeming to be an exception.

Though I did some more checking with Blade Ward. I checked and under Pact of the Tome I didn't have the option to add it to the character. But it was available when selecting Warlock cantrips. (In both cases, trying to use this account as DM to add it to a character in a campaign to the others' character.) So it seems like Pact of the Tome might just be where the issues are for this.

So for curiosity I decided to also try adding the Magic Initiate (Druid) feat. And again, couldn't do Thorn Whip there nor Blade Ward with Magic Initiate (Warlock). So I guess it's a general thing that things requiring an option (Pact of Tome / Feat) require the account the character belongs to having direct access to the desired spell whereas otherwise a DM can add it even without content sharing.

Technically speaking, you shouldn’t even be able to add the feat to the character sheet without content sharing. Without content sharing the only things those other accounts should be able to access is the free content from the Basic Rules & SRD, and theEEPC, plus whatever homebrew you might have in your collection.