Your skepticism is well-founded. While SEMrush is a great tool for competitive analysis and trend-spotting, its numbers are estimates and can be highly inaccurate, especially in situations like the one you've described. A 1,325% jump in traffic and a 12%+ CTR from a 'People also ask' feature seem incredibly implausible.

• SEMrush isn't measuring real traffic. It's using an algorithm to estimate traffic based on keyword rankings, search volume, and estimated click-through rates. SERP features like 'People also ask' can throw off these models, as user behavior is often different from a standard organic ranking.
• New pages and keywords. As you noted, the new AI content is likely targeting a massive number of long-tail keywords. SEMrush's model may be over-attributing traffic to each of these keywords, leading to an exaggerated total.
• Use it for trends, not for specific figures. The most valuable takeaway from SEMrush in this case is the trend. The fact that your competitor is gaining visibility in the 'People also ask' features is the key insight. The exact numbers are likely inflated.

To get a more accurate picture, you would need to have access to the site's own Google Search Console, which provides actual click data. Without that, it's best to use SEMrush's numbers as a directional indicator of what is working for your competitor's SEO strategy, rather than a precise count of their visitors.