feat(eslint-plugin): [prefer-nullish-coalescing] add support for assignment expressions

[abrahamguo]

PR Checklist

• [x] Addresses an existing open issue: fixes #10145
• [x] That issue was marked as accepting prs
• [x] Steps in Contributing were taken

Overview

Re-applies #5234, while accounting for updates made since to prefer-nullish-coalescing.

Commits:

• [x] Extracted the current logic of the LogicalExpression listener into checkAssignmentOrLogicalExpression
• [x] Pulled in other changes to rule file, as well as updates to checkAssignmentOrLogicalExpression to support assignments
• [x] ported over test cases and updates to test case generation functions
• [x] changed all declare consts to declare lets — it is not clear to me why @JoshuaKGoldberg did this in #5234, but I have done it

[typescript-eslint[bot]]

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[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 86.16%. Comparing base (c8e7c27) to head (22841da). Report is 2 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #10152      +/-   ##
==========================================
- Coverage   86.18%   86.16%   -0.02%     
==========================================
  Files         430      430              
  Lines       15029    15031       +2     
  Branches     4360     4361       +1     
==========================================
- Hits        12952    12951       -1     
- Misses       1725     1728       +3     
  Partials      352      352              

Flag	Coverage Δ
unittest	86.16% <100.00%> (-0.02%)	:arrow_down:

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
...lint-plugin/src/rules/prefer-nullish-coalescing.ts	97.70% <100.00%> (-2.30%)	:arrow_down:
packages/rule-tester/src/utils/config-validator.ts	27.41% <100.00%> (ø)
packages/type-utils/src/TypeOrValueSpecifier.ts	100.00% <ø> (ø)
packages/type-utils/src/builtinSymbolLikes.ts	4.91% <ø> (ø)
.../src/typeOrValueSpecifiers/specifierNameMatches.ts	100.00% <ø> (ø)

[JoshuaKGoldberg]

I'd switched from const to let for consistency, I think. Not a major preference.