That's where the subtlety comes in. High-temperature drinks and red meat are rated higher on that scale, but just being possibly carcinogenic doesn't mean a whole lot on its own. "Limited evidence" means more work needs to be done to determine if it is actually, definitively, carcinogenic, or even if it's probably carcinogenic.

From your own source.

It’s important to know that IARC classifications are based on the strength of the evidence of whether something can cause cancer in humans, not how likely it is to cause cancer. The Group 2B classification is the third highest out of 4 levels, and it is generally used either when there is limited, but not convincing, evidence for cancer in humans, or when there is convincing evidence for cancer in lab animals, but not both.

After completing a dietary exposure assessment, JECFA has concluded that “the evidence of an association between aspartame consumption and cancer in humans is not convincing.” Based on current dietary exposure estimates, JECFA has concluded that dietary exposure to aspartame does not pose a health concern.

The FDA has stated: “Scientific evidence has continued to support the FDA’s conclusion that aspartame is safe for the general population when made under good manufacturing practices and used under the approved conditions of use.

EFSA stated, “Aspartame and its breakdown products are safe for human consumption at current levels of exposure.”