Thieves' Cant isn't a written language, thus there would be nothing to understand via a spell.
Nowhere in the quote you've pulled (or the PHB) is thieves' cant ever described as a written language. This is because thieves' cant is both verbal and physical communication. Some word substitution (1 to 1) is used, but it is largely based on metaphor and contextual meaning and a big part of this is the hand symbols used when speaking. D&D's basis for thieves' cant is both historical and a trope.
The symbols mentioned are more like pictographic signs than words.
As such they are not translated, but identified, similar to how we use symbols such as the biohazard sign and nuclear sign to signify specific danger or how the symbols on a crosswalk signify when to wait and when to go. The closest living example of this I can highlight would be Hobo symbols that survive and are still in use today in the US. Different symbols would mean different things to different groups and insider knowledge for understanding thieves' cant symbols would be a must.
Drow sign language isn't an officially included language in D&D 5e rules, at least not as far as I can find.
The languages a PC knows are determined by their race and, save for a special few, are mostly listed on page 123 of the PHB. You'll notice that's there's no mention of a drow sign language. It's not even mentioned in the Sword Coast Adventurer's Guide (a 5e sourcebook for campaigns set in the Forgotten Realms).
If you also look at the references for the Wikia page you've linked you'll notice that it's mostly referencing novels by R.A Salvatore set in the Forgotten Realms and previous editions of D&D. In general, a novel does not equal a rules books for a TTRPG. Even the other question from this site that you've linked is asking about 3.5e, not 5e.
In terms of how much influence a novel does have on rules created for a TTRPG, well, that will be determined by your DM and the world they set their campaign in.
However, this doesn't mean your drow can't know drow sign language. It just means that, by default, it doesn't know it because it's not a part of the rules.
A DM is free to create their campaign setting, their world, their universe, their multiverse, however they please. If you want your drow the know sign language, talk with the DM; see if it's something they think would make sense in their world and if they can incorporate it.
The DMG even has a section on languages, from page 20-21:
When fleshing out your world, you can create new languages and dialects to reflect its unique geography and history. You can replace the default languages presented in the Player's Handbook with new ones, or split languages up into several different dialects. [...] You might invent additional secret languages, besides Druidic and thieves' cant, that allow members of certain organizations or political affiliations to communicate.
Best Answer
You can choose exotic languages at character creation
At first glance this question seems pretty straight forward:
The use of the word obscure would seem to imply to me that an exotic language is a legitimate starting pick.
But wait, there's a complication..
Talking about langauges more generally, the SRD says:
GM permission? Could there be some restrictions, after all?
So do you need permission in order to create an Adventurers League character with an exotic langauge? No.
This quote from the DDAL FAQ (on page 4), in a question specifically about selecting languages at character creation, seems to clear up any uncertainty:
Great news for lovers of exotic languages.
P.S. Following discussion in the comments:
This might not be RAW guidance as explicit as finding a text saying...
..but in the absence of a RAW argument that exotic languages should be prohibited, it makes sense, following the reasoning in my answer, to consider it Rules as Intended that exotic languages are allowed as racial picks.