It looks like you're encountering multiple issues related to Git and Homebrew. Let's break them down and address them one by one:

### 1. **Git Repository Access Issues**
The error messages indicate that Git is having trouble accessing the Homebrew repository, both via HTTPS and SSH.

#### HTTPS Access Issue:
```plaintext
error: Unable to get pack file https://mirrors.aliyun.com/homebrew/brew.git/objects/pack/pack-ec3e2d08567e62eeb002a423e5d4214af4ba196b.pack
transfer closed with 98158874 bytes remaining to read
error: Unable to find eaf887656ffb8e9e35ccf08081814d4735637564 under https://mirrors.aliyun.com/homebrew/brew.git
Cannot obtain needed object eaf887656ffb8e9e35ccf08081814d4735637564
while processing commit c071c779134c3cfb86f82189afda781c66aa2edc.
error: fetch failed.
```

This suggests that the mirror you're using (`mirrors.aliyun.com`) might be having issues or is incomplete. You can try switching to the official Homebrew repository or another mirror.

#### SSH Access Issue:
```plaintext
[email protected]: Permission denied (publickey).
fatal: Could not read from remote repository.

Please make sure you have the correct access rights
and the repository exists.
```

This error indicates that Git is trying to use SSH to access the repository, but your SSH key is either not set up correctly or not added to your GitHub account.

### 2. **SSH Key Issues**
The command `ssh-keygen -R domain.example` is used to remove a host from the `known_hosts` file, which is unrelated to the current issue. However, the subsequent error suggests that your SSH key might not be properly configured.

### Steps to Resolve:

#### Step 1: Switch to the Official Homebrew Repository
1. **Change the Homebrew remote URL:**
   ```bash
   cd $(brew --repo)
   git remote set-url origin https://github.com/Homebrew/brew.git
   ```

2. **Update Homebrew:**
   ```bash
   brew update
   ```

#### Step 2: Set Up SSH Key for GitHub
1. **Generate a new SSH key (if you don't have one):**
   ```bash
   ssh-keygen -t rsa -b 4096 -C "[email protected]"
   ```
   Follow the prompts to save the key (default location is fine).

2. **Add the SSH key to the SSH agent:**
   ```bash
   eval "$(ssh-agent -s)"
   ssh-add ~/.ssh/id_rsa
   ```

3. **Copy the SSH key to your clipboard:**
   ```bash
   pbcopy < ~/.ssh/id_rsa.pub
   ```

4. **Add the SSH key to your GitHub account:**
   - Go to [GitHub SSH keys settings](https://github.com/settings/keys).
   - Click "New SSH key" or "Add SSH key".
   - Paste the key from your clipboard into the "Key" field.
   - Give it a title and click "Add SSH key".

5. **Test the SSH connection to GitHub:**
   ```bash
   ssh -T [email protected]
   ```
   You should see a message like: `Hi username! You've successfully authenticated, but GitHub does not provide shell access.`

#### Step 3: Retry Homebrew Update
After setting up the SSH key, try updating Homebrew again:
```bash
brew update
```

### Additional Notes:
- If you still encounter issues, you can try using a different network or VPN, as some network configurations might block or interfere with Git operations.
- Ensure that your Git is up to date by running `git --version`. If it's outdated, consider updating it.

By following these steps, you should be able to resolve the issues and successfully update Homebrew.