You have to be able to write code in order to be a web developer. However, all websites and digital solutions are developed for people by people, so developing people-centered skills will serve you far better than focusing on code alone.
This isn't an introvert vs. extrovert question, and I don't think either one has an advantage over the other. It is about the following:
There are three groups of people you are serving:
The people who are visiting your website need to have a good experience in order to accomplish their goals. These people have varying abilities, world views, and ways of interacting with your website.
Choose technology and a development style that makes it as easy as possible to build a website that is usable and accessible to as many people as possible.
If you're a developer and content manager, then it might not matter as much. However, if you have non-developers managing content on the website, then you need to choose technology and build it in a way that makes it as easy as possible for them to do their jobs.
Sometimes this coincides with the people who are maintaining the website, and sometimes it doesn't. Either way, you are building the website to help solve a problem for people, and choosing the technology and how you build it affects how well you can solve their problems.
If you're a solo developer, then choosing the technology you're most comfortable with is usually the go-to solution. Unless there's a technology that you don't know as well but the client will pay you to learn it and implement it because it solves their problem.
If you're working as part of a team, think about:
Do they specialize in certain languages and systems? Might you need to subcontract out some work to another developer or company? It could be that the perfect solution to your client's problem is a system that you and your team are not familiar with, so subcontracting work could come in handy.
If you specialize in certain languages and systems, what tools do you use to collaborate? Do you use a specific version control system? Project management? Communication?
Do you have certain coding standards so that everyone is on the same page and all code has a similar style, making it more readable and maintainable across the board?
It's incredibly easy to get caught up in which programming languages you should learn. There's so much chatter, especially on Twitter, about which languages are "best" and what a developer needs to know.
At the end of the day, solving problems for people is your job, and choosing the best technology for the job for your unique set of circumstances and people involved is the name of the game.
All programming languages, stacks, and content management systems are tools to get the job done. Choose which one works best for your problem. For your people.