Add unit tests for "staying on the same page when switching versions" functionality

This is meant to simplify checking correctness of code like #7227 and fixing bugs like #7226. In fact, I'm hoping to eventually make this code general enough that it runs locally with `mike serve`.

I picked `mocha` as the testing library because its Typescript support
relies on ts-node, which this project already relies on. I have little experience with `mocha` vs `jest` vs something else beyond this commit.

See also https://github.com/mochajs/mocha-examples/tree/main/packages/typescript

Instead of using `chai`, I'm using Node's assert package.
Its TS types are in `@types/node`. It should be trivial, and might be good, to switch to `chai` or something else.

This setup is not perfect, in particular I can't get tests to import the whole `index.ts` file. This is why the function being tested gets its own file. Importing `index.ts` would seem to require writing some DOM shims and be a general headache.

For the record, using `tsx` and `jsdom-global` instead of `ts-node` to run `mocha` seemed like the most promising approach, but it still failed since some files imported from this `index.ts` rely on the DOM having some particular structure in their top-level definitions.

Here's how to set up `tsx` and `jsdom-global`, for reference:

```diff
diff --git a/.mocharc.json b/.mocharc.json
index e713305556...347580c924 100644
--- a/.mocharc.json
+++ b/.mocharc.json
@@ -1,6 +1,6 @@
 {
     "$schema": "https://json.schemastore.org/mocharc.json",
+    "require": ["tsx", "jsdom-global/register"],
     "extension": ["ts"],
-    "spec": "src/**/**.test.ts",
-    "require": "ts-node/register"
+    "spec": "src/**/**.test.ts"
 }
diff --git a/package.json b/package.json
index ecc9f98cf9...10242ca725 100644
--- a/package.json
+++ b/package.json
@@ -76,6 +76,7 @@
     "gitlab": "^14.2.2",
     "google-fonts-complete": "jonathantneal/google-fonts-complete",
     "html-minifier": "^4.0.0",
+    "jsdom-global": "^3.0.2",
     "material-design-color": "^2.3.2",
     "material-shadows": "^3.0.1",
     "mocha": "^10.6.0",
@@ -99,6 +100,7 @@
     "svgo": "3.0.0",
     "tiny-glob": "^0.2.9",
     "ts-node": "^10.9.2",
+    "tsx": "^4.16.2",
     "typescript": "^5.5.2"
   },
   "engines": {
```

I can also incorporate the diff into this commit.

Author: ilyagr

.mocharc.json

@@ -0,0 +1,6 @@
+{
+    "$schema": "https://json.schemastore.org/mocharc.json",
+    "extension": ["ts"],
+    "spec": "src/**/**.test.ts",
+    "require": "ts-node/register"
+}