Please describe what the rule should do:

Suggest the use of logical assignment operators.

What new ECMAScript feature does this rule relate to?

Logical Assignment

What category of rule is this? (place an "X" next to just one item)

[ ] Warns about a potential error (problem)
[x] Suggests an alternate way of doing something (suggestion)
[ ] Other (please specify:)

Provide 2-3 code examples that this rule will warn about:

Bad:

opts.foo = opts.foo ?? 'bar'

Good:

opts.foo ??= 'bar'

(same for ||= and &&=)

-- Optional extras --

Bad:

if (!a) {
  a = 'foo';
}

Good:

a ||= 'foo';

Bad:

opts.baz ?? (opts.baz = 'qux');

Good:

opts.baz ??= 'qux';

Why should this rule be included in ESLint (instead of a plugin)?

It's a general syntax suggestion.

Are you willing to submit a pull request to implement this rule?

Not at this time.