For me if you are going to hold them in one had doing so horizontally distributes their weight better so puts less pressure/weight m on you and them. Good to do so over the water, the net or your lap as well just on the off chance you drop them although once you develop a technique I find you don’t drop many, apologies to those early fish I caught as a youngster ?
Then if they’re bigger then I find a cradle grip is better or just laid in the net. Always knelt down as well just in case you stack it although luckily I’m of an age where my balance hasn’t gone yet ?
Quite a bit bigger and I just leave them in the net and take some of their weight with the net rather than have their full weight on the ground plus you can quickly lift the net if they move.
It’s almost as important to hang onto some bigger fish for a little while in the margins to revive them if they’ve scrapped a bit. There’s also something quite satisfying feeling their power through your arm once they are ready to go.
Others may have more lax or more stringent methods but such methods have always seen the fish go back strongly.