```ts
export function applyOverrides(base: Record<string, string>, overrides: string[]): Record<string, string> {
  if (!Array.isArray(overrides)) {
    throw new Error("overrides must be an array");
  }

  const merged = { ...base };

  for (const override of overrides) {
    const [name, value] = override.split('=', 2);

    if (typeof name !== 'string' || name.length === 0) {
      throw new Error("override names must be non-empty strings");
    }

    if (typeof value !== 'string') {
      throw new Error("override value must be a string");
    }

    if (!base.hasOwnProperty(name)) {
      throw new Error(`base does not contain setting "${name}"`);
    }

    merged[name] = value;
  }

  return merged;
}
```