When upgrading to Angular 13, I received "peer @angular/cli@">= 12.0.0 < 13.0.0" from @angular-eslint/schematics@12.6.1" error. After investigation we found that upgrading @angular-eslint/* to next packages will make the upgrade work. (https://github.com/angular-eslint/angular-eslint/issues/796).
Problem is, we cant use the next versions in production. So needed to understand the repercussions of forcing the build. If not, then removing eslint packages from the package.json.
Regards CSR