Overpass - Get ways around me with details

Hi, for my application I need the ways around me (e.g. in a 2000m radius). At the moment I have the following query (Overpass):

<query type="way">
   <around lat="40.65541" lon="-4.70717" radius="2000"/>
</query>
<union>
  <item/>
  <recurse type="down"/>
</union>
<print/>

From this query, I get nodes and ways. Example of a way:

  <way id="305251304">
    <nd ref="634163717"/>
    <nd ref="3098509510"/>
    <nd ref="3660108566"/>
    <tag k="highway" v="residential"/>
    <tag k="name" v="Calle Valladolid"/>
    <tag k="source" v="ITACyL"/>
    <tag k="source:date" v="2009"/>
  </way>

My first problem is that I need more details (name, ref name, maxspeed...) for the ways. At the moment, I make another request to Nominatim for each way, e.g.:

https://nominatim.openstreetmap.org/lookup?format=json&namedetails=1&osm_ids=W305251304

This takes too long. Is it possible to get the details for all the ways already in the Overpass query? If not, is there another API which I can use for my requirements? By the way: I have installed Nominatim and Overpass on my own server because I send many requests.

My second problem is that I just need streets, I don't need e.g. cycleways, footways and buildings. How can I manage this in my query?