See my post in the answers section.
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This is also happening to our app in homescreen. I reproduced this with using standalone page with select element. I submitted a feedback to apple. Hopefully we get some response. For reference, see below the details I submitted to apple:
The problem is around the select element not showing the options when clicking on it. On first launch of the home screen app, the select element is still working. But after minimising and reopening it, the select element seems to become unresponsive and does not show the options.
Steps to reproduce:
Create a standalone page with select element.
Clear the browser cache of Safari thru the settings.
Using Safari, visit the page and add to Home Screen.
Launch the Home Screen app. Observe that the select element is clickable and options are showing.
Minimise the Home Screen app. Then re-open it. Observe that the select element does not seem to respond, and the options are not showing.