[field controls] Respect validationMode

[atomiks]

Closes #1050

[mui-bot]

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[mj12albert]

Don't think it's directly related to this PR, but I couldn't make a required checkbox group because required is a prop on individual checkboxes but not on CheckboxGroup:

// a combination of the CheckboxGroup and Field demos
export default function FieldCheckbox() {
  return (
    <Field.Root>
      <Field.Label>Pick one or more</Field.Label>

      <CheckboxGroup defaultValue={[]}>
        <label>
          <Checkbox.Root name="fuji-apple">
            <Checkbox.Indicator>
              <CheckIcon />
            </Checkbox.Indicator>
          </Checkbox.Root>
          Fuji
        </label>

        <label>
          <Checkbox.Root name="gala-apple">
            <Checkbox.Indicator>
              <CheckIcon />
            </Checkbox.Indicator>
          </Checkbox.Root>
          Gala
        </label>

        <label>
          <Checkbox.Root
            name="granny-smith-apple"
          >
            <Checkbox.Indicator>
              <CheckIcon />
            </Checkbox.Indicator>
          </Checkbox.Root>
          Granny Smith
        </label>
      </CheckboxGroup>

      <Field.Error match="valueMissing">
        You must pick at least one
      </Field.Error>
    </Field.Root>
  );
}

[mj12albert]

https://codesandbox.io/p/sandbox/sweet-brattain-q9ptqr

When I make a required RadioGroup that has no initially checked radio and tab through it without checking any of the radios, it doesn't trigger an error state (I logged some stuff and it seems the validation functions are being called)

Also when the required RadioGroup is wrapped in a Form (with a submit button), if I click the submit button without touching the RadioGroup the error doesn't appear which could be the same issue?

However when a radio is checked, the console.log in the Form's submit handler doesn't log the value 🤔

[atomiks]

Are these bugs (with CheckboxGroup as well) related to this PR or are they on master as well? If on master, we can create a new issue for them to separate the work