On the GeoServer admin page, it is possible to restrict the Spatial Reference Systems (SRS) that can be requested in WMS GetMap requests by putting a comma separated list of SRS numbers in the input box at http://localhost:8080/geoserver/web/?wicket:bookmarkablePage=:org.geoserver.wms.web.WMSAdminPage (set server and port according to your server).
In consequence, only the specified SRS numbers can be used for the SRS parameter in GetMap requests (all others will not get a valid response). Besides, limiting GeoServer to only a few SRS that are really needed by your application will shorten the GetCapabilities document significantly because a very long list of all available SRS is included by default when there is no limit set.
Is there any possibility to set this limit via GeoServer's REST Api? Unfortunately, I could not find any example on this in the documentation.