I felt way more empathetic during the first year my son and my daughter were born, but I feel like I lost that part of me. I kinda miss it
I realize that sounds silly but it really does work. A lot of emotional behavior is muscle like and setting aside intentional practice will lead to longterm change.
1. Set a trigger to engage in the practice like "When I hang out with my kids immediately after the work day"
2. Do the practice. Try to be empathetic to your kids small daily issues. At first, like all newish things this will feel silly but over time it will feel natural.
Obviously try to be genuine. If your kids plight of someone snatching their favorite toy or whatever doesn't move you, don't force it. Just try to practice visualizing yourself in their place. Don't go "fake empathetic kid tone".
While during their first year, my initial reaction was usually the correct one. I felt I could "read" them better.
You have the right goal in your focus, you'll get it with time and practice.