```typescript
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 result = { ...base };

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

    if (!value || typeof name !== 'string' || !override.includes('=')) {
      throw new Error(`Invalid override: "${override}"`);
    }

    if (!result.hasOwnProperty(name)) {
      throw new Error(`Override for non-existent setting: "${name}"`);
    }

    result[name] = value;
  }

  return result;
}
```