### Description

Replace the existing selects with multi-selects that allow you to filter multiple DAG run states and types at the same time, somewhat similar to my prototype:

![image](https://github.com/apache/airflow/assets/1842905/c4ec0793-1ccb-417d-989c-781997416f97)


### Use case/motivation

I'm not sure if it is just me, but sometimes I wish I was able to show multiple DAG run states, especially `running` and `failed`, at the same time. 
This would be especially helpful for busy DAGs on which I want to clear a few failed runs. Without the multi-select, if I switch from `failed` to `running` DAG runs, I need to orient myself again to find the run I just cleared (assuming there are lots of other running DAG runs). _With_ the multi-select, the DAG run I just cleared stays in the same spot and I can check the logs, while clearing some other failed runs.

I'm not sure we need a multi-select for DAG run types as well. I'd tend to say no, but maybe someone else has a use-case for that.

### Related issues

_No response_

### Are you willing to submit a PR?

- [X] Yes I am willing to submit a PR!

### Code of Conduct

- [X] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

"""Home view."""
        from airflow.models.dag import DagOwnerAttributes
        hide_paused_dags_by_default = conf.getboolean("webserver", "hide_paused_dags_by_default")
        default_dag_run = conf.getint("webserver", "default_dag_run_display_number")
        num_runs = request.args.get("num_runs", default=default_dag_run, type=int)
        current_page = request.args.get("page", default=0, type=int)
        arg_search_query = request.args.get("search")
        arg_tags_filter = request.args.getlist("tags")
        arg_status_filter = request.args.get("status")
        arg_sorting_key = request.args.get("sorting_key", "dag_id")
        arg_sorting_direction = request.args.get("sorting_direction", default="asc")
        if request.args.get("reset_tags") is not None:
            flask_session[FILTER_TAGS_COOKIE] = None
            
            return redirect(url_for("Airflow.index"))
        cookie_val = flask_session.get(FILTER_TAGS_COOKIE)
        if arg_tags_filter:
            flask_session[FILTER_TAGS_COOKIE] = ",".join(arg_tags_filter)
        elif cookie_val:
            
            return redirect(url_for("Airflow.index", tags=cookie_val.split(",")))
        if arg_status_filter is None: