How does allowImportingTsExtensions work with moduleResolution: "bundler" and .ts imports?

Question presented to candidate: "Some projects write import { twice } from \"./math.ts\" with the .ts extension. What does allowImportingTsExtensions actually allow, why does tsc insist on noEmit or emitDeclarationOnly with it, and when is this a good idea?"

What a strong answer should cover:

• Without the flag, a value import ending in .ts, .mts or .cts is TS5097; with it, tsc accepts the path and type-checks against the source file
• tsc never rewrites import paths (before 5.7), so emitted JavaScript would keep "./math.ts" and fail to load; that is why the flag requires noEmit or emitDeclarationOnly (TS5096)
• It fits setups where something else runs or builds the .ts files: Vite or esbuild with moduleResolution: "bundler", Bun, Deno, and Node.js type stripping
• import type with a .ts path is allowed even without the flag; importing a .d.ts path as a value is TS2846
• Emitted .d.ts files keep the .ts specifiers; .js specifiers still work alongside
• TypeScript 5.7 added rewriteRelativeImportExtensions, which rewrites ./math.ts to ./math.js in the output, for projects that do want tsc to emit JavaScript

Code / implementation expected: Optional — a tsconfig with the flag and noEmit, and an import that needs it.