My SV07 had a similar problem, moving the eccentric adjuster on the roller behind the nozzle to increase tension solved my problem.
Then perform the “paper test”, being sure to save settings tight after. This should save a new Z offset to printer.cfg. Once saved then “home all” and lower your nozzle to 0.
Watch the light on the sensor during the Z tilt adjust procedure. Does it flicker or blink other than when the nozzle is close to the bed? NOTE the switch distance is not adjustable. Mine switches when the nozzle is 3.5mm (or so) above the build plate.
I keep mine with the left rear snugged down. This bolt passes through the strain relief for the bed heater cables. That causes it to be the first one to bottom out. Tighten all 4 1 turn at a time until the LR gets “tight”. Back off a tiny bit then run the “screw height” macro. If you touch the square where the The LR adjustment shows KlipperScreen will 0 that square and recalculate the others. Run “screw height” over and over until it is as good as possible.
Home all
Z tilt adjust
Bed mesh
Paper test (again)
Save and restart.
I only run bed mesh when I have first layer issues NOT every print. I use Christian Vicks “Printer additions”. The package includes macros to mesh the bed at several temperatures then load the closest one during the “start print” process. It has worked flawlessly for me.