chore: enable prefer-nullish-coalescing internally

[JoshuaKGoldberg]

PR Checklist

• Addresses an existing open issue: continues Repo: Enable prefer-string-starts-with internally #7338
• That issue was marked as accepting prs
• Steps in Contributing were taken

Overview

Fixes up most of the last few violations of @typescript-eslint/prefer-nullish-coalescing. Ignores primitives because we tend to do "fun" things with strings.

[typescript-eslint]

Thanks for the PR, @JoshuaKGoldberg!

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[bradzacher]

Can we turn it on with ignoreConditionalTests?
I think that using ?? in conditional tests is less clear.

Consider the downlevelled output:

if (x || y) { }

// vs

if (x ?? y) { } 
// downlevelled to
if (x != null ? x : y) { }

I think it's a whole lot less clear.
Actually I'm going to go as far as advocating for flipping the default in v7 - #8243