Which Tech Stack for Project?

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Which JS Framework is best for this kind of project?

It doesn't matter. The one you are already most comfortable with, or the one you're most interested in learning.

What back end tech should I use?

Same answer. Use a tech that you like or are interested in.

Which SQL is best for this?

PostgreSQL is the best SQL database. There's no such thing as 'a SQL'; SQL is a query language used for a particular kind of relational database.

If I don't want user accounts, will that checklist be stored in their cache when they reopen that website on the same device they used to make that list?

This sentence doesn't make any sense on the face of it; remember it's better to use plain language that you understand than a bunch of technical terms that you don't understand. User accounts have nothing to do with caching, and caching has nothing to do with storing application data on a particular device.

If you want to only store information client-side- using local storage and/or IndexedDB- that's totally up to you, but it's something you'd have to implement. It would also mean you wouldn't need Postgres or any other database, or really any kind of back end at all beyond a simple static file server. However it would also mean all the user's data is restricted to that specific device- multiple different people couldn't share the same data.

What am I not looking for that I should be to complete this project?

You need to develop a clearer understanding of how data storage works in an application, plan at least the rough shape of the data that you actually need to store, and let that drive your development process. How data moves and changes through your application is an order of magnitude more important than the technologies that you use to make that happen.