I was going to say you do it by getting a reference to the map object, but I don't think that's needed. But I have left that in at the base of this response as it a very helpful thing to know.
try the following:
var map = L.map('map', {
zoomsliderControl: true,
zoomControl: false,
layers: [layer]
}).setView([57.7, 11.9], 8);
Where 'map' is the id of the Map element.
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On your Map element get a reference to the map object.
<Map ref={(m) => this.leaf = m} etc...>
then in your react component.
where you have componentDidMount= () =>{
use the map object to add in the slider
var map = this.leaf.leafletElement;