The biggest factor here is almost certainly the lens, not Canon vs Nikon body sharpness.

You’re comparing zooms (especially a long-range 18-135mm) against a 35mm f/2 prime, and primes are usually sharper than zooms. Zooms with shorter ranges also tend to outperform long-range zooms. Lenses are often sharpest when stopped down a stop or two from wide open, so aperture also matters in comparisons.

There can be small body-level differences: some Canon DSLRs were known for stronger anti-aliasing filtering and sometimes more aggressive noise reduction, both of which can make files look a bit less crisp. But those effects are usually smaller than lens differences.

Since you tested on a tripod and in RAW, that already removes motion blur and most JPEG-processing differences from the equation.

To get similar sharpness on the Canon, try a comparable prime lens and compare at the same focal length and aperture. That will make the test much fairer. In short: yes, switching to a fixed-focal-length lens would very likely improve perceived sharpness, especially compared with consumer zooms.