You really think so? I agree with you that there are many deficiencies in the Australian constitution, plus a national tradition of constitutional conservatism which means most attempts to address these deficiencies are doomed to fail. But in calling it "categorically the worst", I think you go too far.
I think the (unwritten) UK constitution is worse. Similar to the US Supreme Court, the High Court of Australia has the power to overrule the Australian Parliament and nullify unconstitutional legislation, even though it uses that power somewhat sparingly. By contrast, the UK Parliament is "sovereign", which means the courts cannot overrule Parliament. The UK courts effectively have the power to strike down primary legislation contrary to EU law, but with Brexit that power is going away. They also have the power to issue a "declaration of incompatibility" saying that legislation violates human rights, but that does not by itself void the legislation – either Parliament must act to amend or repeal the legislation, or there is also a fast track procedure whereby ministers can amend it without going to Parliament, but until either Parliament or the ministers act the legislation stays in force. (Also, Parliament granted the courts this power, and can take it away at any time by a simple majority vote in each House.)
I think another way the Australian constitution is superior to the UK constitution is that the Australian constitution bans the national government from establishing a religion (the ban doesn't strictly speaking apply to the state governments, but in practice they abide by it), whereas the UK constitution establishes a state church in one of its four constituent countries (England).
Also, the UK Parliament has in theory unlimited power to overrule or even abolish the devolved administrations (Scotland, Wales, Northern Ireland) at any time, by a simple majority vote (even though real world political constraints mean that trying to use that power could easily lead to the violent breakup of the UK). By contrast, the Australian Parliament can't legally abolish the states without a national referendum which would be very unlikely to pass.
The UK, in my opinion, is a totalitarian state and has no pretense to being a free society - so yeah, I don't include it in this set, as you rightfully indicate. Australia is a step above the UK in this respect - as the UK is a highly classist, authoritarian/totalitarian state where a majority of its population live in servitude to feudal lords, it doesn't even pretend to have a Constitution, nor individual rights. Australia does pretend, though, so its just a bit above the UK in that regard ..
I think your phrase "racism is intrinsically encoded in Australian law" accurately describes the legal situation up until the reforms of the 1960s and 1970s. But I'm not convinced it is an accurate description of Australian law in the present-day. Can you give some examples of present-day Australian laws which in your view "intrinsically encode" racism?
Section 25 reads:
"25. Provisions as to races disqualified from voting:
For the purposes of the last section, if by the law of any State all persons of any race are disqualified from voting at elections for the more numerous House of the Parliament of the State, then, in reckoning the number of the people of the State or of the Commonwealth, persons of that race resident in that State shall not be counted."
Section 51 (xxvi) reads:
"51. Legislative powers of the Parliament:
The Parliament shall, subject to this Constitution, have power to make laws for the peace, order, and good government of the Commonwealth with respect to: ... (xxvi) the people of any race for whom it is deemed necessary to make special laws;"
Then, there was the abolishment of ATSIC in 2005, which many in the indigenous community view as a betrayal. Even the UN got involved ..
And .. then there is the Nauru situation. Its essentially a detainment camp for undesirable immigrants, and has recently been removed from public scrutiny by way of being made a military base. Still people suffering in that camp daily, but you won't hear many Australians being too deeply bothered by the fact that their government is running a concentration camp... well, its one of 7 that are in operation, and I can guarantee you they won't get public oversight any time soon.