$ npx tsc
This outputs sources with correct relative links:
$ jq . dist/background.js.map
{
"version": 3,
"file": "background.js",
"sourceRoot": "",
"sources": [
"../src/WebExtension/background.ts"
],
"names": [],
"mappings": ";AAEA,OAAO,CAAC,OAAO,CAAC,WAAW,CAAC,WAAW,CAAC,GAAG,EAAE;IACzC,OAAO,CAAC,GAAG,CAAC,4BAA4B,CAAC,CAAC;AAC9C,CAAC,CAAC,CAAC"
}