Describe the bug
This might be a follow-up to #480. I noticed that initially the inspector correctly omits values in the request that are optional and not filled out. However, when I change the value to something and then remove the value again (so I have an empty textfield), the inspector sends "" instead of not sending the value at all.

To Reproduce
Steps to reproduce the behavior (simplified):

1. Using the Go SDK, I have the following argument definition:

Price         uint32   `json:"price,omitempty" jsonschema:"Some description"`

2. When running List Tools, I get the expected result:

{
  "tools": [
    {
      "name": "search",
      "description": "Something",
      "inputSchema": {
        "type": "object",
        "properties": {
          "price": {
            "type": "integer",
            "description": "Some description"
          }
        },
        "required": [],
        "additionalProperties": {
          "not": {}
        }
      },
    }
  ]
}

3. Invoking the tool, I see the correct request not containing the argument:

{
  "method": "tools/call",
  "params": {
    "name": "search",
    "arguments": {},
    "_meta": {
      "progressToken": 0
    }
  }
}

4. Afterwards I write 0 in the price field and delete it again. If I now run the tool again, an empty string is sent for the integer price field.

{
  "method": "tools/call",
  "params": {
    "name": "search",
    "arguments": {
      "price": "",
    },
    "_meta": {
      "progressToken": 1
    }
  }
}

Expected behavior
If I enter anything for an optional field and delete the value again, it should not be sent in the request (like initially).

Additional context
I tested both v0.16.1 and the latest commit from this repository. Both have the issue.