axe-testcafe | The helper for using Axe in TestCafe tests | Accessibility Testing library

The documentation for axe-core states that you need to specify which rules you intend to test against using axe.run options.

Landmarks are discussed in WCAG 1.3.6., which is a "Level AAA" item. It appears that axe-core is only capable of testing against "Level A" and "Level AA." In your example, the item is not listed by the tool as a WCAG failure, but rather a best-practices recommendation. This may be why it isn't showing up in your other tools.

If you can easily implement this recommendation, then I'd say go ahead and do it. If not, I wouldn't let something like this stop my code from going into production. Landmarks are nice-to-have, but it's far more important that you meet all "Level A" requirements and as many "Level AA" requirements as you reasonably can.

It's worth noting that any automated accessibility testing tool is nothing more than a starting point for manual evaluation. These tools often generate tons of false positives (and sometimes miss important things!) because it's often not possible to algorithmically determine whether something is genuinely useful to human visitors.

I've also seen pages/apps that pass automated tools with no errors (Wave, Axe, etc.), but they are completely impossible to use with assistive technology.