I received an answer from AWS support and the issue has been resolved. It turned out that the problem was related to the nameservers.
My domain is hosted on AWS, but my backend is in Google Cloud. While configuring my backend I must have changed the default nameservers on AWS to the ones provided by Google:
ns-cloud-c1.googledomains.com.
ns-cloud-c2.googledomains.com.
ns-cloud-c3.googledomains.com.
ns-cloud-c4.googledomains.com.
The AWS support advised me to switch back to the default ones provided by AWS, because they were specified by whois lookup:
ns-1553.awsdns-02.co.uk
ns-857.awsdns-43.net
ns-91.awsdns-11.com
ns-1160.awsdns-17.org
One of the beta testers, who previously experienced connection problems, reported that he was able to use the app on WiFi without any problems.
As a side note, I have also been shown a handy tool to inspect how different locations resolve an IP address of a domain:
https://www.whatsmydns.net/#NS/apple.com
FYI @eskimo and thanks again for your input!