Here (on Debian) it stops trying to connect after 2 minutes [...] although the default connect timeout value seems to be 5 minutes according to the DEFAULT_CONNECT_TIMEOUT macro in lib/connect.h.
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A default value for --max-time doesn't seem to exist, making curl wait forever for a response if the initial connect succeeds.
I use the web interface for update and there are no errors, it just hangs.
I waited for 5 minutes without success.
Then the Pi-hole is no longer accessible thru the interface.
Well, there is a failsafe, but maybe you have found a special install or situation where it is not able to catch the error properly. Please run the command