I ended up using shopify init to create a new project with the Remix template and merged that with my existing project, which seems to have done the trick, with the added benefit of using current versions of all dependencies.
Somewhere, something must have gone wrong on my end. It would just be nice if the error would reflect that, instead of the odd ‘3rd party cookies’ message.
Thanks for taking a look!
Side-note: I’ve always wondered: when you use the Remix template you also get a page in app/routes/_index/route.tsx with some text like “A short heading about [your app]”, but this page is not used in Shopify and seems to only be available locally, what is it for?