[Bug]: Subsequent signature requests from the test dApp lead to an error stating: Error: Request of type 'eth_signTypedData' already pending for origin metamask.github.io.

**Describe the bug**

When experimenting with various signature requests, both the Extension and Mobile app may encounter a scenario where subsequent actions from the test dApp lead to an error stating: "Error: Request of type 'eth_signTypedData' already pending for origin metamask.github.io. Please wait." This message indicates that a previous request of the same type is still being processed, and the system requires completion of this action before proceeding with any new requests.

**Expected behavior**

Sequencing signature requests efficiently

**Screenshots/Recordings**

**Steps to reproduce**

1. Connect to[ test dapp](https://metamask.github.io/test-dapp/)
2. Initiate several signature requests

**Error messages or log output**

```shell

```

**Detection stage**

In production (default)

**Version**

7.38.0

**Build type**

None

**Device**

iPhone 15, Samsung S24 Ultra, emulator

**Operating system**

iOS, Android

Start by reproducing the sequence in the linked test dApp on the listed iOS and Android environments, using repeated eth_signTypedData requests. Trace the mobile app's handling of pending signature requests; done means subsequent requests can be completed without the already-pending error.

Written by the indexing model from the issue text.