servers don’t need to be exposed to the Internet for it to act as such, it can be bound to a local port, which you do if you want to do local webdev, or communicate via some IPC (inter process) mechanisms
programming languages are fairly rigid in that they are parseable, so the code editor just send your code for every interval via IPC to the “lang servers”, where it will parse your code and send back a detailed response of its structure in some standardised format that your code editor understands, without it actually know how to parse it
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