Water line size advice on new basement bath?

I'm installing a half bath in my basement and I need advice on tapping into the existing lines. I have a 3/4 in main line leaving the water heater, then it branches out to fixtures on the first floor to 1/2 in lines, and the 3/4 inch continues upstairs to feed those fixtures. Is it okay if I tap into one of the half inch lines feeding the first floor for my basement half bath?
Also I was going to use shark bite T's for tapping in, has anyone used thses before?

General rule of thumb, two fixtures on a 1/2" line. Lots of houses have more and work okay; just depends on what flows are required. A half-bath won't be using much. Better if you can probably tap into the 3/4" line and then run 1/2". See what the pros have to say...

I would come off the 3/4 lines to feed your new bath, that way you will
not be losing the volume to your other fixtures.

What is the penalty of having 3/4" water line fed by a 1/2"?

Thanks

Lower pressure and volume.
I would tap off of the 3/4" with 1/2" hot and cold.