Is share of model a Google ranking?

No. It is a count of mentions inside generated answers. Two brands can hold similar rankings and very different shares of model.

How often should it be checked?

Often enough to notice a change in who gets named. The answers move when new pages are published and when assistants update.

What is share of model?

Share of model is the share of AI answers in a category that name your brand. It is share of voice for answer engines. You measure it by asking the same buyer questions across assistants and counting how often you are the brand they name.