When I make a change to the headers using the UI and watch the server tab and check the payload, it's not sent in the patch payload, and I never see those settings in a GET Tool request. The payload when saving changes to custom headers looks like this:

{
  "function": {
    "name": "33242fasdfaaDDfdf",
    "async": false,
    "description": "asdfasdgadasdfasdf",
    "parameters": {
      "type": "object",
      "required": [
        "testProp1"
      ],
      "properties": {
        "property here": {
          "description": "dasdfasd",
          "type": "string"
        },
        "testProp1": {
          "type": "string",
          "description": "test descr"
        }
      }
    }
  },
  "messages": [
    {
      "type": "request-start",
      "content": "Just a sec while I try."
    },
    {
      "type": "request-failed",
      "content": "I wasn't able to put it through, sorry."
    }
  ],
  "server": {
    "url": "https://test.com",
    "timeoutSeconds": 30
  },
  "async": false
}

https://cdn.discordapp.com/attachments/1211484481848873020/1346527076588589126/image.png?ex=67c88290&is=67c73110&hm=8d3e1b204dc14137bd7f21580c6a0e4d76d98d8773400c2a8fedd219fa0b9f6f&