I'm not familiar with that site specifically, but in principle using a web/cloud tool means that your being on mobile has zero impact on the output. You are feeding a more powerful computer prompts and it sends you back the pictures it generates. So this isn't a "mobile" problem.
There's two things to keep in mind though - Firstly, using SD is a art in itself. It's not easy to get good outputs. I know it's kinda presented as being "just type and awesome comes out", but typically a lot of work goes into generating good AI art works. There are a lot of parameters and a lot of possible tools and you do need to spend some time learning how it all fits together. Secondly, running on someone else's platform is always limiting in terms of what parameters you can fiddle with. A big chunk of getting good results is being able to use your own preferred embeddings, LORA and model to get the results you want. SD can do photorealistic aliens and cartoon smut, but it can't do both on the same settings, and if you can't change them then you will always be limited.
You don't necessarily need to move off of mobile, and at least while you are starting out I wouldn't recommend spending lots of money, but you should think about SD as being a workflow and consider what is convenient. Personally, I would work on a laptop if at all possible, even if you are just using the various cloud versions (HuggingFace etc). That's just because you are going to do a lot of copying and pasting and granular tweaking of settings. When you have a big prompt and you need to just change one value, having a trackpad is a lot easier than poking at tiny text on a small screen.
I do generally believe that running a personal instance of SD is the way forward in the long term. The real barrier is technical knowledge more than cash/gpu power; setting it up is not easy if you are someone who doesn't know Python (like me). If you have any device with a mediocre gpu (I started on my laptop 3050ti) then SD will run slow, but will actually run. If you already have that device to use, it's literally free and you get the benefits of a local instance immediately, like being able to do big runs (leave them overnight if they take too long) of X/Y plots to help you learn how parameters work, and being able to try out models and LORAs to get where you want to be.
If you don't have such a device, you can still dip your toe in without spending a lot of money. I do my SD work on a Shadow.tech cloud PC and various other services are available. Yes, in this economy throwing 50 bucks around isn't nothing, but you get a GPU with 20gigs of VRAM and it runs 10x faster (more actually - 10 iterations per second instead of 4 seconds per iteration) than I had before.
You can access any cloud instance via mobile if that's your bag, although it does not work wonderfully on Shadow, because it's so focused on giving you a Windows desktop rather than a mobile front end. You could however be a super cool guy and connect your phone to a USB-C hub, then connect it to a mouse, keyboard and monitor.
All just food for thought :D