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`.

Picked `mocha` as the testing library because its Typescript support
relies on ts-node, which this project already relies on.

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`.

Author: ilyagr

.mocharc.json

@@ -0,0 +1,5 @@
+{
+    "extension": ["ts"],
+    "spec": "src/**/**.test.ts",
+    "require": "ts-node/register"
+}