Looks like you have some lint failures you'll need to clean up too:

This type is not allowed in the 'if' condition because it could be undefined. Allowed types are boolean or boolean-or-undefined. (strict-boolean-expressions)
  87 | 
  88 | const isEmptyOrContainsOnlySuper = (node: ts.ConstructorDeclaration, options: Options): boolean => {
> 89 |     if (node.body) {
     |        ^
  90 |         const { unnecessarySuperCall } = options;
  91 | 
  92 |         if (!containsStatements(node.body.statements)) {

Looks like you have some lint failures you'll need to clean up too:

This type is not allowed in the 'if' condition because it could be undefined. Allowed types are boolean or boolean-or-undefined. (strict-boolean-expressions)
  87 | 
  88 | const isEmptyOrContainsOnlySuper = (node: ts.ConstructorDeclaration, options: Options): boolean => {
> 89 |     if (node.body) {
     |        ^
  90 |         const { unnecessarySuperCall } = options;
  91 | 
  92 |         if (!containsStatements(node.body.statements)) {

Done

A good start!
Left some comments on requested structural changes and missing test changes.

Done

@JoshuaKGoldberg @adidahiya ???

testNext failure is unreleated. I'd like to release this and improve it in future PRs if necessary