Is there a Material-UI component to search/select tags like in stackoverflow?

You can do that with the Autocomplete component by overriding the ListboxProps of the Listbox which is the container of the dropdown and set the CSS grid to display 3 equal width columns using the fr unit:

<Autocomplete
  ListboxProps={{
    style: {
      display: "grid",
      gridTemplateColumns: "1fr 1fr 1fr",
      maxHeight: "initial",
    }
  }}

Now assuming the option has the following type:

type TagOption = {
  tag: string;
  views: number;
  description: string;
};

In the Stackoverflow dropdown, there are only 6 options at max, so we need to restrict the number of options shown in the Listbox:

import Autocomplete, { createFilterOptions } from "@mui/material/Autocomplete";

const _filterOptions = createFilterOptions<TagOption>();
const filterOption = (props, state) => {
  const results = _filterOptions(props, state);

  return results.slice(0, 6);
};

<Autocomplete filterOptions={filterOption}

We also want to create a customized option component for each grid item. Here is a minimal example without any much styles to get you started:

function OptionItem({ option, ...other }) {
  return (
    <li
      {...other}
      style={{
        display: "block"
      }}
    >
      <div>
        <Chip label={option.tag} />
        {option.views}
      </div>
      <div>{option.description}</div>
    </li>
  );
}

renderOption={(props, option, { selected }) => (
  <OptionItem {...props} option={option} />
)}

And finally set the isOptionEqualToValue and getOptionLabel to ensure that the option get filtered properly and the input display the correct tag when selected:

isOptionEqualToValue={(option, value) => option.tag === value.tag}
getOptionLabel={(option) => option.tag}

Live Demo (Source)

That's not a perfect fit, but you can use autocomplete (using multiple, customizable and asynchronous)