npm install --save-dev mochawesome mochawesome-merge mochawesome-report-generator

you should update cypress-parallel scripts

"cy:run:parallel": "cypress-parallel -s cy:run -t 3 -d 'cypress/e2e/ui/' -r 'cypress-mochawesome-reporter' -o 'cypressParallel=true' -p 'reporter-config.json' --strictMode false && npm run merge-reports"

add merge-reports scripts

"merge-reports": "mochawesome-merge cypress/reports/*.json > cypress/reports/merged-report.json && marge cypress/reports/merged-report.json -f merged-report -o cypress/reports"

example reporter-config.json

{ "reportDir": "cypress/reports", "overwrite": false, "html": false, "json": true }

you will take a one report in merged-report.html