both have 2 elements -- an integer and a string (you can disregard the brackets and commas inside the string)

No, it shouldn't. It's an array with 3 elements, there is no nesting structure there.

This test seems incorrect:
[1,'[',']'] same as ['[',']',1]: False should equal True
According to the examples, this should be False

I can't determine from the kata description what assumptions we are allowed/expected to make. I don't think we can assume that a subdomain will be 'www' - and you cannot assume what a subdomain might be, so you realy must start from the TLD. Once the effective TLD is determined, get the domain and ignore any subdomains if there is one.

This is kind of a non-trivial problem that requires the use of the "requests" package to rerieve the list of effective top-level-domains from https://publicsuffix.org/list/public_suffix_list.dat

That is not a spoiler - the url should have been in the question, of the question should have explicitely given either a list of TLDs or Subdomains.

Poorly written question.