Based on your setup in Google Play Console there are a few ways to test if the integration is correct.
If Play App Signing is not enabled for your app which means that you are using your own keystore to upload and distribute your app or game to users via Google Play Store, the easiest way to test the update functionality is to build an apk / app bundle directly from Unity and install on your test device, but keep in mind that you should check those items first:
In-app updates are available only to user accounts that own the app. So, make sure the account you’re using has downloaded your app from Google Play at least once before using the account to test in-app updates.
Make sure that the app that you are testing in-app updates with has the same application ID / package name.
Because Google Play can only update an app to a higher version code, make sure the app you are testing as a lower version code than the update version code.
Make sure the account is eligible and the Google Play cache is up to date. To do so, while logged into the Google Play Store account on the test device, proceed as follows:
If Play App Signing is enabled for your app you can test the integration in two ways.
First by uploading apk / app bundle files directly to Play Store Console in Alpha channel and use this channel to download the update and test the app. The downside of this method is that you will have to update your versionCode every time when you want to test changes in the integration. If it's not a big deal for you I would prefer to go with this way.
Second way is by using Internal App-Sharing option from Play Store Console. You can read more about it here: https://support.google.com/googleplay/android-developer/answer/9844679
Here are the steps you should follow with this method:
On your test device, make sure you've already installed a version of your app that meets the following requirements:
The app was installed using an internal app sharing URL
Supports in-app updates
Uses a version code that's lower than the updated version of your app
Follow the Play Console instructions on how to share your app internally. Make sure you upload a version of your app that uses a version code that's higher than the one you have already installed on the test device.
On the test device, only click the internal app-sharing link for the updated version of your app. Do not install the app from the Google Play Store page you see after clicking the link.
Open the app from the device's app drawer or home screen. The update should now be available to your app, and you can test your implementation of in-app updates.
You can read more about this topic in Google's documentation: https://developer.android.com/guide/playcore/in-app-updates#internal-app-sharing