Conclusion: I don't like boiling the onions in beer. If you cook down the onions afterwards, it concentrates the flavor of the beer in them. Instead, I would prefer an actual pan sauce. (AKA 'bangers and mash)
This is an extremely common way to cook the three together. Unfortunately, it tastes far too bitter for me.
A traditional British dish is đŸ“–bangers and mash (AKA sausages and mashed potatoes), often served with onion gravy.