I've now tried it on my Steam Deck and it works well. I just press the Playstation button and an action button (cross in my case) for 5 seconds and it connects.
The only downside for now is that I have to use the cable to reconnect to the Playstation afterward. There might be a way to progam another action button to reconnect to the Playstation, but I haven't found it yet.
Edit: solved the reconnection to the PS5 problem
Settings>Accessories>General>Bluetooth Accessories>press the action buton (square, cross, triangle or round) and home buton for 5 seconds
It’l program an entry that you have to use every time you want to reconnect to the Playstation. I think you can’t do it without a second controller though.