In the form I stated, this is true, to get Play you must ship Google Search, and must do so on all of your devices.
What is not true, but implied by the EU ruling is that, a) Android (as defined as purely AOSP) is incomplete and unusable without Google apps, b) that other app stores do not exist for Android, c) that other search engines somehow magically don't work on Android.
None of those are true. I find it unfortunate that Android does not have higher profile alternative options, but no one else seems to want to put as much effort into their products as much as Google has.
Google's actions simply do not meet any reasonable definition of being a monopoly. Google's only action is requiring the entire Google Apps suite shipped on a device as an all-or-none license, it does not require the end user to use them, it does not prohibit the end user from installing others or disabling built in apps, it does not require signing into a Google account to use the device, it does not prevent APK sideloading.
And, until recently, Google was not even a phone OEM (and arguably still isn't, as they do not build their Pixels, HTC and LG do), and Pixels are not nearly as popular as Samsung Galaxy S series (which are famous for "ruining" the Android experience by using tons of custom Samsung apps), and LG G and V series, and Motorola phones dominating the mid-tier segment, and China and India being largely Xiamoi, Huawei, and BBK (Oppo, OnePlus, and Vivo).
Worldwide, Samsung and BBK are the #1 and #2 phone manufacturers, and they merely use Android as their OS. At what point did the EU have the authority to say Google had a monopoly when they do not sell Android phones in any reasonable capacity.