Buffer

Below we set processes with a function in a QTimer.singleShot, to allow multi-execution, but it is not mandatory according your context.

Buffer with 4326 point layer, so with fake units:

import os
import shutil
 
myPath = r'C:\\Users\\georg\\Downloads\\'
 
project = QgsProject.instance()
project.removeAllMapLayers()
project.clear()
iface.mapCanvas().refresh()
 
crs = QgsCoordinateReferenceSystem.fromEpsgId(4326)
project.setCrs(crs)
project.setEllipsoid('EPSG:4326')
 
peaks = QgsVectorLayer(myPath + 'peaks_selection/peaks_selection.shp', 'Peaks', 'ogr')
QgsProject.instance().addMapLayer(peaks)
 
# Buffer function
def myBuffer():
    # Directory for created layer
    _peaks_buffer = myPath + '_peaks_buffer'
    if os.path.isdir(_peaks_buffer) == True:
        shutil.rmtree(_peaks_buffer)
    if os.path.isdir(_peaks_buffer) == False:
        os.mkdir(_peaks_buffer)
 
    # Buffer on peaks
    peaks_buffer_path = _peaks_buffer + r'\\peaks_buffer.shp'
 
    processing.run('qgis:buffer', { \
    "INPUT": peaks, \
    "DISTANCE": 0.05, \
    "SEGMENTS": 10, \
    "END_CAP_STYLE": 0, \
    "DISSOLVE": False, \
    "OUTPUT": peaks_buffer_path})
 
    # Open the buffer layer
    peaks_buffer = QgsVectorLayer(peaks_buffer_path, "Buffer area", "ogr")
    project.addMapLayer(peaks_buffer)
 
    # Register layer
    my_buffer = project.mapLayersByName("Buffer area")[0]
 
    # Buffer below
    root = project.layerTreeRoot()
    myBelowLayer = root.findLayer(peaks_buffer.id())
    myClone = myBelowLayer.clone()
    parent = myBelowLayer.parent()
    parent.insertChildNode(-1, myClone)
    parent.removeChildNode(myBelowLayer)
 
# Run function with delay
QTimer.singleShot(200, myBuffer)