repro

package.json

@@ -10,6 +10,8 @@
     "@types/node": "^12.20.12",
     "@types/react": "^17.0.5",
     "@types/react-dom": "^17.0.4",
+    "dexie": "^3.1.0-alpha.10",
+    "fake-indexeddb": "^3.1.2",
     "react": "^17.0.2",
     "react-dom": "^17.0.2",
     "react-scripts": "4.0.3",

src/db.test.ts

@@ -0,0 +1,29 @@
+import Dexie, { DexieOptions } from "dexie";
+import indexedDB from "fake-indexeddb";
+import IDBKeyRange from "fake-indexeddb/lib/FDBKeyRange";
+
+interface IMessage {
+  id?: number;
+  message: string;
+}
+class TestDatabase extends Dexie {
+  messages: Dexie.Table<IMessage, number>;
+
+  constructor(options?: DexieOptions) {
+    super("Database", options);
+    this.version(1).stores({
+      messages: "++id",
+    });
+    this.messages = this.table("messages");
+  }
+}
+
+test("should pass", async () => {
+  const db = new TestDatabase({
+    indexedDB: indexedDB,
+    IDBKeyRange: IDBKeyRange,
+  });
+  const result = await db.messages.put({ message: "a message" });
+  console.warn(result);
+  expect(result).not.toBeUndefined();
+});

src/fake-indexeddb.d.ts

@@ -0,0 +1,2 @@
+declare module "fake-indexeddb";
+declare module "fake-indexeddb/lib/FDBKeyRange";