If you are concerned about the foot plant impacts having a negative impact on your recovery, I suggest you get some good running shoes with good resilient soles. This can take a lot of impact out of your foot plant.

There are some gait symptoms that are directly related to how the brain processes movement/proprioception, etc. More lift off the toes is not uncommon.

You may benefit from orthotics. They can help the foot support your weight better. The simplest would be the Dr Scholl's orthotic insoles that you can get at Walmart after standing on the Dr Scholl's orthotic measuring device. I have used similar orthotics for 30 years. They help the ball of my foot absorb more of my foot plant.

As Lara said, I doubt the impact is hurting your brain even though it may feel uncomfortable. A good Physiatrist (Physical Medicine and Rehabilitation Doctor) knows how to diagnose gait issues related to neurological problems.