Is there any need to screw a sliding patio door in or can it just be fixed with expanding foam?
Depends.
Do you want the patio door to remain fixed in the hole or to fall out when somebody leans on it?
Really? I thought this stuff was supposed to be solid.
If it's in England you need to get Building Control involved if you DIY, too.
The foam holds it very solidly. No way will it fall out even with a rugby team pushing on it. That said it isn't UV stable or rodent proof so extra fixings can be prudent. Most modern doors have brackets that slot in rather than having to drill right through the frame. They are so easy to fit that you might as well.
As waswas says it is technically a building regs matter. They won't actually do anything but it might get flagged up when you sell the house. No idea why you can fit floors, build walls, replace electrics and plumbing all by yourself but need someone checking up if you try and fit a window.
Fixing will also aid in squaring the frame to allow better/smoother operation where as with foam theres no 'fixing' till its gone off
I've done a few in the past - I'd get a few mechanical fixings into either side + top and bottom - use the foam as a secondary fixing once you've proved everything slides/operates as it should.
The guys who fitted both our sets of bi-fold doors a couple of years back didn't use any foam - they said it makes adjustment/moving/removal so much harder.
I'd get them set in place true using the wedge shaped plastic packers, then secure using expansion bolts. Foam is just to fill the gaps to make them air tight, not to secure them.