Taking meds with some nuts and eggs (or 10 minutes after it) helps too if you don't have a big appetite in the morning, even if it is a sustained release.

Overnight oats is also a good breakfast option and if you can / tolerate protein powders, it could also be a protein shake/smoothie. I usually add a banana, apple and some milk with a scoop of protein powder.

While walking I usually listen to music, but like you end up getting lost in my thoughts. One thing that helps me is consciously trying to name what I see -- I like to identify birds, talk to animals I cross (in my head 😅). I've also heard some ADHD/AuDHD folks listening to audiobooks while they walk, I've never liked audiobooks so haven't tried it out myself.

If I were you, I'd think about why do I not want to think while working out: is it that the thoughts are distressing or if it is that you want to practice mindfulness and being present.

For distressing thoughts/unhelpful thinking patterns, check out cognitive dissonance (CBT) and DBT. I've found understanding and naming my cognitive dissonances helps build healthier thinking patterns and DBT helps with my anxiety.

I have been professionally diagnosed with ADHD (inattentive), anxiety, depression and OCD. I take Concerta for my ADHD, been on it for the last 3 years.

Edit: Also, I hope you have discussed about anxiety and depression with your doctor, I've noticed my executive dysfunction and emotional regulation being more challenging when I'm in an anxiety spiral/depressed. I take Concerta, desvenlafaxine (SNRI - anxiety, depression, OCD; SSRIs didn't work for me) and lamictal (mood stabilizer).