Issues with Heating with brand new carrier

I got a new carrier hvac unit late last year because I was told it was a good deal. My old hvac unit was working fine but was over 22 years old. We were also the very last house in our HOA with the original hvac unit so rather than dealing with an emergency we looked into hvac units.

We had no issues in the summer or fall but during winter, my Google nest kept saying there was no power. I originally worked with Google on trying to address with no success. I called the same hvac technician and he found that the furnace was cutting power to my Google thermostat.

He said we needed to wait for a part to getting it fixed. When he came, he cut a big square and said that there wasn't enough air going through which is why the furnace would shut off. He was going to add a vent in the cut area to allow for the air to get in much easier. This makes no sense as the original vent looks fine and we never had this issue with our old hvac unit.

Can someone please let me know if this hvac technician and/or carrier is the problem?