Which valve fitting / adapter combination can i use to connect the kitchen faucet and undersink water filter to the cold water line

I purchased an underink water filter:
KOHLER Aquifer Under-Sink Double Cartridge Water Filtration System

I was using the plastic connection that came with it:

Connected like so:

The top connects to my faucet (plastic male to female connection), and the blue plastic hose push connects to the KOHLER water filter which connects to my fridge's water line

The fitting is leaking where it threads into the water valve (plastic female to male connection). I took the fitting to lowes/home depot and tried to attach it to newer valves but it would always spin in place when trying to connect. I suppose the threads got damaged.

Please, how can I combine a brass fitting to replace this setup? I don't mind having to use several adapters

In the photographs of the water filter I noticed they used an adapter as well:

The closest thing I could find in lowes was a male to push adapter:

This is my water valve after some disconnections:

I am pretty sure its 3/4 inch for all connections (this may be incorrect according to manual stating 3/8 inch water supply connection.

The OD of the blue plastic tube is 3/4 though the push connection is labled 3/8.
Could you please point me to the parts I need to fix this issue? I currently have turned off my cold water supply because the leak is really bad.

Thank you