TL;DR: Try https://play.google.com on a web browser using the account set as the parent in your family group set in Family Link.
Many Internet-based services nowadays are cross-platform, which means that they have apps for Web, the App Store, and the Play Store, and some could even also have apps for Windows, Mac, Linux, etc. There is no standard; it's completely on each service provider what they offer their audience / user to deliver their service.
As of November 2023, localization and personalization have become more sophisticated. Internet-based services might show slightly different options based on the user's location and other settings. Because of this, I highly recommend you look at the related help resources directly from one of your devices and use your account, in this case, the account set with parent privileges.
Google Family Link has an online service brochure with the following address https://families.google/familylink/ and a web app with the following address https://familylink.google.com.
Google Play also has a web app. Its address is https://play.google.com. I suggest first accessing Google Play using a web browser on a laptop, a desktop computer, or another device with a screen large enough so you can have the desktop experience as on devices with small screens, using the mobile experience some options might be harder to find. Your mileage might vary.
I suggest you review the Family Link brochure / microsite and review it thoroughly.
Still, you might go directly to the FAQ or go to the Google For Families Help Center, which has a topic about Family Link and topics for other related services. In the Google products Help Center, a topic is a category of help articles.
It's worth noting that the Google for Families Help Center, as of November 11, 2023, has a link to Guidebook for Family Link