You’re right that European nuclear is not "independent" if that means "mined entirely inside Europe". But the dependency profile is not the same for Russian pipeline gas. Uranium is globally traded, compact, cheap to stockpile relative to the energy it contains, and available from several non-Russian suppliers (Kazakhstan, Canada, Namibia, Australia...). The harder choke points are conversion, enrichment, and reactor-specific fuel fabrication.

Europe does have uranium resources, for instance the Salamanca/Retortillo project, but the constraint is permitting, environmental acceptance, waste handling, and political legitimacy rather than geology. So the honest claim is not "nuclear makes Europe autarkic". It is "nuclear gives Europe a more diversifiable and stockpilable dependency than gas, provided Europe also invests in mining, conversion, enrichment, and fuel fabrication capacity".

Europe managed to get off Russian Gas, but didn’t manage to get off Russian uranium industry. You correctly identified the chokepoints and Russia can’t be replaced fast there.