An update does not come in separate files. Its one firmware image, similar to an iOS update. Which functions have changed or what is new and should be tested is mentioned in the release notes here in the forum.
Regarding your problem:
Some networks are slow in connecting, which could lead to timeouts and connection retries. This could also be the reason why you are asked twice to connect. What exactly is going on can only be diagnosed when you send log files to the support team through the Nuki App.
When you are part of the beta the Smart Lock will also create additional logs and report some of the in real time to Nuki, which will help to do faster & better diagnosis.
The latest beta does also contain WIFI stability improvements, which might solve your problems at all.