The Yahoo article lists numerous possible causes of the few thousand extra deaths, none of which are related to vaccination. For instance, there were 23 million fewer GP visits in 2020 compared to 2019. And most of causes of the additional deaths saw large decreases during the pandemic. Additionally, elective operations fell by 3.5 million from March 2020 to February 2021.

Also, in your first link, Figure 2 seems to contradict what you're saying. Higher vaccination rates do lead to fewer covid cases per 100,000 people.