Studies around children and screen time:
https://health.choc.org/the-effects-of-screen-time-on-children-the-latest-research-parents-should-know/
https://www.unicef.org/parenting/child-development/babies-screen-time
https://www.hackensackmeridianhealth.org/en/healthu/2023/09/11/screen-time-and-developmental-delays

The argument of "my kids watched TV and they're fine" is idiotic at best. A few decades ago, cars didn't have seat belts. Since people survived without seat belts, will you stop using them?

Hopefully four mos later you have found a new family to work for. One who shows you respect op!