That would be the react way to achieve this:

export default class Test extends Component{

  constructor(props) {
    super(props)

    this.state = {
      selectOptionValue: '1'
    }
  }

  handleOnChange = (e) => {
    this.setState({
      selectOptionValue: e.target.value
    })
  }

  render(){
    return (
      <div>
        <select defaultValue = "1" onChange={this.handleOnChange}>
          <option value="1" >Option 1</option>
          <option value="2" >Option 2</option>
        </select>

        <select  disabled={ this.state.selectOptionValue === '2' }>
          <option value="a" >January</option>
          <option value="b" >Febreaury</option>
        </select>
      </div>
    )
  }
}

How about onChange event from this ? For your convenience:

class FlavorForm extends React.Component {
  constructor(props) {
    super(props);
    this.state = {value: 'coconut'};

    this.handleChange = this.handleChange.bind(this);
    this.handleSubmit = this.handleSubmit.bind(this);
  }

  handleChange(event) {
    this.setState({value: event.target.value});
  }

  handleSubmit(event) {
    alert('Your favorite flavor is: ' + this.state.value);
    event.preventDefault();
  }

  render() {
    return (
      <form onSubmit={this.handleSubmit}>
        <label>
          Pick your favorite La Croix flavor:
          <select value={this.state.value} onChange={this.handleChange}>
            <option value="grapefruit">Grapefruit</option>
            <option value="lime">Lime</option>
            <option value="coconut">Coconut</option>
            <option value="mango">Mango</option>
          </select>
        </label>
        <input type="submit" value="Submit" />
      </form>
    );
  }
}

If you want to keep it simple and use pure javascript, you could just use the following snippet.

document.querySelector('select[ref="selectOption"]').addEventListener('change', function(e) {
  document.querySelector('select[ref="selectTime"]').disabled = (e.target.value === '2') ? true : false;
})

<select ref="selectOption">
  <option selected value="1">Option 1</option>
  <option value="2">Option 2</option>
</select>

<select ref="selectTime">
  <option value="a">January</option>
  <option value="b">Febreaury</option>
</select>

Here's another approach to define which state variable needs to be set.

state = { someStateVariable : "" }

render() {
    return (
        <select onChange={event => this._setSelected({ someStateVariable: event.target.value })}>
            <option value="1">One</option>
            ...
        </select>
    );
}

_setSelected = newState => {
    this.setState(newState)
}

Step 1 - Create state and set initial value an empty string

      const [category,setCategory] = useState('');

Step 2 Map youre options and check id in the option value === select value then set selected to true

  const renderedResults = results.map((result) => {
    const selected = category === result.id ? "true" : '';
    return (
      <option selected={selected} key={result._id} value={result._id}>{result?.name}</option>
      );
  });

Step 3

 <select
   onChange={(e) => {
    setCategory(e.target.value);
   }}
   className="form-select"
   aria-label={"Default select example"}
   >
   <option value="">Select a category</option>
     {renderedResults}
 </select>