Read the CSV row by row using the csv module, create an empty line layer, create and insert LineStrings.
This is the exact contents of my CSV file:
[[7.89471262378373, 48.405478200932436], [7.896052894441773, 48.41059537964788]]
[[7.89471262378373, 48.405478200932436], [7.892694850981679, 48.40550448264249], [7.887506712484601, 48.40574772233518], [7.878533768291611, 48.4055148846117]]

import csv
file = r'/home/bera/Desktop/lines.csv'
#Create empty temp line layer
vl = QgsVectorLayer("LineString?crs=epsg:4326&index=yes", "myLayer", "memory")
provider = vl.dataProvider()
with open(file, newline='') as f:
reader = csv.reader(f)
for row in reader:
#row is a list of strings: ['[[7.89471262378373', ' 48.405478200932436]', ' [7.892694850981679', ' 48.40550448264249]', ' [7.887506712484601', ' 48.40574772233518]', ' [7.878533768291611', ' 48.4055148846117]]']
coordinates = eval(','.join(row)) #Join the string with a comma delimiter and turn into a list with eval
line = QgsGeometry(QgsLineString(coordinates)) #Create a line geometry
f = QgsFeature() #Create a new feature
f.setGeometry(line) #Set the geometry
provider.addFeature(f) #Add it
QgsProject.instance().addMapLayer(vl)
