How to handle alone time as a couple when you have a pug?

Those of you in relationships, how do you go about keeping your alone time as partners when you have a pug, especially when they are a puppy?

We adopted our pug ( >1yr neutered male) after folks close to us couldn't keep him, and as we already have a small-breed dog we figured the companionship couldn't hurt. We weren't fully prepared for just how affixed to one single person pugs are. I say this because I want to make it clear that while yes, we threw ourselves into the deep end with a breed we have never had before, we would never give him up. He has only been with us for a little under 3 months but he is a forever member of our family.

We have slowly been able to leave him in a partitioned-off area (with the older dog – no behavioral issues there) while my partner and I run errands, but we have never been gone than longer than a few hours unless one of us stays home since he is still a puppy. If he sees us during this time though (like when we come through the door) he begins his pug screams until he can get to us. You can imagine how this could impact a relationship in more intimate moments.

I've looked around on different subreddits and google results, but haven't really gotten a clear answer besides "just ignore them."

Any advice, tips, tricks, anything, would help greatly. We have a snugglepup plush coming any day now, but would appreciate any and all input.