Or have I completely misunderstood how a Republic rather than a democracy works? The issue isn’t republic vs democracy, but federal state (with a balance of power between a central government and its individual regions) vs unitary state (where the national government holds power and delegates or devolves specific rights and responsibilities to its regions). Individual US states - or Australian states or Canadian provinces or Swiss cantons - have powers that the UK's devolved administrations can only dream of.
Nevertheless, popular claims that Roe v Wade had to be overturned as abortion rights aren’t clearly protected by the US Constitution and therefore must revert to the states are untrue. In addition to its Constitution, the USA has a body of federal law, passed by the two US Houses of Congress and signed into law by the President, that states cannot violate or limit. (Federal law can’t violate the Constitution; both Constitutional law AND federal law are arbitrated by the Supreme Court.)
Many federal laws deal with necessary nationwide competencies, e.g. determining how to declare war, or who holds citizenship. But some are designed for the equal protection of all citizens, for example the Americans With Disabilities Act, the Civil Rights Act, and the Voting Rights Act (which guarantees specific voting rights to citizens which can’t be abridged even in a state or local election). The federal level can also act to prevent states from making laws that breach its own international obligations, such as human rights. The UN has already stated that the USA is now in violation of the International Covenant on Civil and Political Rights. Arguably, the USA may have an obligation to place limits on states criminalsing or excessively restricting abortion, or at least to legislate that they must mitigate the impact so that women are not unlawfully injured or disadvantaged.
In Canada, abortion rights are guaranteed by the Health Canada Act and can't be abridged by the provinces. Provinces can’t make abortion illegal, even solely within their own borders. They can’t add additional restrictions like age limits or time limits. They can’t pass laws that let a parent, spouse, doctor, employer, bio-dad, or rapist (as allowed in some US states) interfere with a pregnant woman’s decision to abort. They must honour the federal commitment to subsidise abortion for those covered by universal healthcare, although healthcare is managed at the provincial level.
The US federal govt CHOOSES not to do any of that. It chooses NOT to protect US women and girls, despite proof that some states have passed dehumanising laws that systemically, disproportionally disadvantage and endanger women and girls. It chose not to mitigate the chaos resulting directly from the decision to overturn Roe v Wade.
Even Poland, when its highest court removed certain existing abortion rights in 2020, provided a grace period. Texas, in contrast, cancelled ALL existing appointments for ANY abortions the same day the legal decision was made, leaving patients in the waiting room and on the operating table, some with no options at all as anyone assisting them in leaving the state to obtain an legal abortion could be charged with a criminal offence. There’s no justification for what the USA has done here that is compatible with or defensible under even the most basic and wishy-washy idea of “feminism”: the idea that women are human beings and full citizens with the right to be treated equitably.
Wasn't there another 'progressive' judge who decided to retire under Trump rather than hanging on until there was a Democrat? Yes; Anthony Kennedy. Not a progressive (he was a Reagan appointee), but a swing vote as newer Republican-appointed justices are even more regressive. His record on abortion was mixed. He'd said he wouldn't strike down Roe v Wade, but so did Gorsuch and Kavanaugh.(There’s a persistent, unconfirmed rumour that AK had top-level persuasion to resign. As is customary in contemporary US politics it involves allegedly illegal activities, on the part of a family member, in the service of an unnamed foreign power whose leader’s name rhymes with gluten.)