Married for 4 years, together for 9. We sometimes get into that rut you describe, where we don't have much exciting going on during the day, our routines are exactly the same day-to-day, and we sink into our phones out of boredom and then suddenly realize there's a sense of loneliness/disconnection.
Most often, our best/most frequent conversations come from:
1. Our shared hobbies/activities. Both DH and I ski and kayak competitively year-round, so we spend a lot of time together training, and talking about upcoming races, our performance at previous races, and technique/skills. We also like camping, hiking, anything outdoors really. This can generate conversations about our future dreams -- where would you want to hike next? How would we prepare for a long through-hike on the PCT? etc.
2. Making an effort to follow along as DH talks about his interests (and he does the same for me lol). I really couldn't care less about electronics, but DH is a computer engineer and is just naturally nuts about it. So I've soaked up enough knowledge from him over the years to have a passable conversation with him about it. I'll even initiate conversations about new speaker models or motherboards because I know he can get onto a roll and then all I have to do is nod and mmhmm once and a while. DH sends me articles during the day about finances and asks my opinion, or he will send me cute baby stuff.
3. Logistical items - we only have one car, and divorced parents, and various family members we like to visit, so planning visits and trips logistically is a good one. We can also deepen this conversation with talking about what we are looking forward to during xyz trip to visit Uncle Bob, etc.
4. Even when we do get into that habit of disengaging and scrolling on our phones, we will often come across a meme or funny video and show it to the other to get them to laugh and talk about how dumb/silly/cute it was. Or we send each other articles that we are reading and think are cool or thought-provoking, and then have a conversation about the subject.
5. Watching movies/TV or listening to podcasts, the subjects will often spark interesting conversations as we ask each other's opinions or viewpoints on what we just watched/listened to. After each episode, we will often turn to each other and spontaneously talk about what parts we enjoyed and which we didn't. Or if I'm feeling mixed about something, I'll ask "what did you think of the part when the characters did ___?"
Some general thoughts/tips:
I find the concept of emotional "bids" for attention to be spot-on. Check out Gottman's theory of bids. Anyway, we both read his book and we both work really hard to "turn toward" any bid for attention/affection either of us makes. That could be a question, a hand squeeze, gesturing for a hug, a look, etc. Initiating a conversation is another bid, and understandably, like you experience, having it kind of fall flat or not be reciprocated is deflating, discouraging, and there's a definite "ouch" feeling.
Making a conscious effort in our relationship to reward these connection attempts has really built a foundation where both of us feel really emotionally connected, intimate, and safe. It is a re-enforcing cycle as well -- the more of these conversations that are welcomed, the more frequently random, smaller, and intimacy-building conversations are initiated. But the more of those conversations that are rebuffed, fewer conversations and connections are initiated. Not because of malice on their part, but simply because it's human nature to be less inclined to converse if you perceive coolness or disinterest.
How to initiate and carry on a conversation, and not only that, but be charismatic and skillfully deepen the conversation to get the other person to open up and engage more fully with you, is a skill you can learn and grow. Because you are the one initiating this new change, you might have to give some grace and understand that your wife may not be very skilled at this yet - but you can coach her a bit :)
Approach your wife with a sense of curiosity. Not just about the events that are going on in her life, but about the human soul inside her. Ask her about her opinion about *everything* - even tiny things. Does she like that shade of blue? Does she like her sushi with tuna or shrimp? What did she think of that scene of the movie you just watched? If she could only choose one, would she rather drink coffee or eat chocolate for the rest of her life? Send her stuff (articles, podcasts, memes) and ask what she thought, and ask probing/more detailed questions if she gives a shallow (rebuff/unskilled) answer. Create change by modeling the behavior you want and giving her an example to follow.
The idea is initiate the conversation, and don't let her off the hook with a curt, shallow, surface-level answer. You need to probe deeper and be really curious about what that human soul underneath really thinks about the subject you brought up. Ask her to clarify, tell you more about her answer, what about xyz angle? Offer your full opinion on the subject as an example, and you can pause while you explain yourself to invite her thoughts as well. But also knowing that you've hit the limit is a skill too -- there are only so many opinions someone can have over whether you are out of milk or if the laundry needs to be done, you know?