The 'do I go back and let him out or wait it out' dilemma is a tough one.
In theory, letting him out when he barks = rewarding the barking = do it again.
However..
He needs to know you're listening, he's safe, all is well. He also doesn't need more frustration, he already can't cope with frustration from general life.
So if you don't let him out swiftly should he bark/whine etc... then a/ he learns people aren't listening/he's not safe and b/ he gets more frustrated.. which in turn leads to more unwanted behaviour.
The gold standard is that they don't bark in the first place, rather than that we ignore it....
However when you have a dog you know well, who is secure and confident and so on and so forth, its possible to determine a 'hey did you really piss off, you bastards, oh well ill go to sleep then' bark from a 'omg the sky is falling in, magpies are about to attack, the end is nigh' bark and the 'oh shouting, imma shout, ive shouted myself into frustration, next comes panic... here we goooo' bark..
Then it can be possible to ignore and let them settle, or respond, as necessary.
So i think in this instance I'd have gone and changed the subject asap, and tried again after time to recover... but hindsight is a wonderful thing and in the moment we have to make a call, and there is always the chance it is the wrong one, we just cannot possibly get it right every time.
If you think he is barking at something, or barking to check you're there, you could just try shouting 'Thanks, I know' or 'Thanks, I am here' (its the tone that will really convey the message).
Some dogs just want to know you are still there, particularly if they haven't actually been all around the house, haven't seen you doing boring things (I recommend they do, but if they're big and silly and liable to trash the place I can see why not, yet!)... then they may really not know whats going on and find that rather difficult.
This is especially true for new/young dogs as we tend to take them with us to do fun things. As they cannot imagine anything they haven't directly experienced... what do they think we've gone to do when we walk out of the room without them? Frustrating as hell if you think anyone leaving the room has gone to do AMAZING FUN SHIT without you!
And some dogs just want to know that you know that they saw something.
Keep muddling on! You're actually doing a fantastic job of this!