What spacing to use between microstrip trace and ground plane on same layer?
The general rule of thumb for clearance either side of microstrip lines is three substrate thicknesses. The reduction of microstrip impedance due to the adjacent ground will be minimal for most purposes other than precision metrology.
There will be some slight coupling of the signal onto the adjacent grounds, so they should be adequately grounded by vias to the microstrip ground, at least every λ/10, to prevent coupling into structures that might become inadvertently resonant at some frequencies.
If you are going to use gaps of less than three substrate thicknesses, then consider designing the line as CPWG, coplanar with ground, for which there are many design resources available.