Following solution 2 works well for me.

For several days now, Aurora Store has been experiencing problems when searching for applications. This is due to limitations put in place by Google. While waiting for a fix, we can advise you the following two workarounds:

Solution 1: Create a 'dummy' Google account, disconnect the anonymous account in Aurora Store, then reconnect using this Google account.

Solution 2: Searching for applications in the browser on the Play Store site:

• Authorize the opening of Play Store links by Aurora: long press on Aurora icon, go to 'App info', then to 'Open by default', activate 'Open supported links', click on 'Add link', select the two proposed links.
• Search for an application on the Play Store site in the Browser, then without going to the application page, long click on the chosen application and click on 'Open link in an external app'. If you go to the application page, you can use the Browser menu (3 dots at the bottom right), then click on 'Open in an app'.

Solution 3: Install the latest development version, which automates the opening of the Play Store page as described above from a search made in Aurora Store.<

Source: iodéOS News