FWIW, I think the most likely culprit will be a change in the version(s) of some module(s) between 5.24.0 and 5.24.1 - as already suggested by Anonymous Monk and localshop.

With Strawberry Perl the LWP version is at 6.15 in both 5.24.0 and 5.24.1, so we should be able to rule it out.
However, IO::Socket::SSL was bumped from 2.027 in Strawberry-5.24.0 to 2.043 in Strawberry-5.24.1.
And Net::SSLeay was bumped from 1.74 to 1.80.

I'd be inclined to update those 2 modules in Strawberry-5.24.0 to the version used in 5.24.1 and see if that fixes the issue.

Of course, there may be other relevant modules that were upgraded from 5.24.0 to 5.24.1, in which case you can continue on with the procedure if the Net::SSLeay and IO::Socket::SSL upgrades don't fix the issue ;-)

Cheers,
Rob