Just buy a 1/2" compression x 3/8 compression and either use the same gray supply line or buy a new one......or buy a 1/2" compression x 3/8" compression shutoff valve. Old plumbing can be fun!
I worked with a plumber for a while as a teen and learned some very valuable things:
1) Always shut off the supply. It's under pressure.
2) Sewage flows downhill. 3) Don't bite your fingernails!
Oh...and it looks more like they used the old copper pipe as a conduit for a new plastic pipe.
OP, you’ve been at this remodel quite awhile now. You’re tired and don’t need more work, if it isn’t broke why would you want to fix it? You know what to do, you know the work involved should you ever have to go into the slab.
You’re pretty much gonna need to jackhammer that entire area out. It’s that simple. Just tear it all out. It may be working fine but that is an unsightly connection that needs replaced.
It’s possible that they had a slab leak and repiped it using the copper as a conduit. Do you know where the manifold is? If so, check it to see if there is a poly pipe connected to it somewhere. Any obvious drywall/ plaster repairs nearby that would indicate that the tied into plumbing there?