[RPG] If I were a poor orphan in Neverwinter, what district would I likely live in

The whole world is a city, and there aren't just ten districts.

The Guildmaster's Guide to Ravnica says that, before the whole world got turned into an urban cityscape, there were originally 10 districts within the City of Ravnica. Other lesser cities had their own districts and so on, which expanded and sprawled until they all touched at the edges to form one vast city, which took on the name of the old capital. But the "Tenth District" as described in the GGtR is not 1/10th of the entire plane, it's just one of the ten districts of the old capital city.

Much of this is covered in the introductory "Welcome to Ravnica" section of the book, in particular on page 8:

The story of Ravnica focuses on its core. Sometimes called the city proper, the core is divided into ten districts [...] Beyond the core are an uncounted number of other districts, which originated as outlying cities that gradually melded into the expanding metropolis. Well-known districts outside the core include the Smelting District, Irbitov (the mausoleum district) and Jezeru (the lake district).

Details on those other districts aren't in this book; I suspect they're references to places from the Magic: The Gathering novels that are set in Ravnica or places represented on specific cards. You may be able to locate some information in published pieces on the MTG website, or on fan-compiled wikis. This article has a small amount of information about some of the names mentioned above, among others, and has links to a few articles that go more in-depth about certain locales. But the quote above does say there are "uncounted" other districts, so that certainly leaves plenty of room for 'make stuff up' as well.

So to go back to your question, what that tells us is that the original City of Ravnica was approximately the size of Luxembourg, which is an absolutely enormous city by our standards, but still only a tiny part of the plane.

The 10th District is intended to be a representative sample of Ravnica as a whole. Beyond the core, there are more districts, more city, more of the same; but maybe less equally distributed. Outside the core, there are large areas that are heavily dominated by one Guild (or a few of them), while the ten districts are an area where all the Guilds have an approximately equal footing, which makes it a good area for adventures and campaigns that draw in characters from many Guilds, backgrounds, and career paths.

It's all city, since that's the theme of the setting, but everything outside the 10th District is really up to the DM to populate as needed -- with more or less guidance from preexisting sources, as you prefer.

For example, you might have a huge area that's completely dominated by Izzet industrial works, where the workers' homes are tucked in and around the tangle of pipes, furnaces, and production lines. In such a place, there may be little or no influence from Guilds like Simic, Gruul, and Selesnya, and even the Azorius and Orzhov have only a minor presence to provide their services to the workers without investing a great deal of time and effort on the place.

In other places, the Golgari might be the primary controlling interest, with a few Simic outposts working in concealed krasis-augmentation laboratories, and not many actual people aside from the overseers of a huge zombie workforce that tends to the gardens.

So yeah, sure, there's plenty of space to have whatever you want, as long as it kinda sticks to the themes of the setting.

The main source of current information about Neverwinter comes from the Sword Coast Adventurer's Guide Chapter 2 under the heading of the same name in the section "The Lords' Alliance" (p. 51-53). It contains a reasonably detailed history and current status as well as a couple of maps (one being a partial world map and one of the city itself).

There is also a small amount of information in Storm King's Thunder here (p. 101), but most of it is also in the above reference and there is no map. The city is even more briefly described and mentioned in Princes of the Apocalypse here (p. 35-36) also with no map.

Note: I have refrained from quoting any of the material since you are asking simply about where it can be found and not any specific information about the city, and it would not be allowed or ethical to quote all the material here.