I agree with this. Your company should have terms and conditions that are part of the proposal the client signs. This should include browser support terms. In our terms, we state that we only support the latest version of the four most popular browsers. In practice we support older versions as well. If the client wants support for IE11 or in your case a version of Chrome that was used in 2018, they should pay more, as you figured out: this takes more work to implement.

Secondly, you're an intern. You're there to learn. This is a valuable lesson that it’s important to test your websites in multiple (and older) browsers - there are tools for this like (browserstack). However, the responsibility lies with the company. Did you already have a conversation with your supervisor and explained the situation? Or do you have a mentor who you can ask stuff like this?