UK LLP + Non-UK Resident + Stripe: Taxation?

Note that the tax situation will depend on the rules of your home countries. Your home country may not see the LLP as transparent.
So you should consult with tax lawyers in your home countries, before setting up such a structure.

What you could also consider as an alternative would be a Swiss verein. This is what many international law firms (e.g., Dentons) use. I don't know how it works in detail though.

You need to investigate this very carefully with an accountant or another tax expert in your country. The rules are constantly being tightened and tax authorities around the world are becoming more and more aggressive, making up stories and unscrupulously lying to get some tax money in the coffers.

The Swiss solution would be a very different setup. It may not even make sense for your situation. All I know is that international law firms often use this model because it allows their offices in different countries to remain separate legal entities, which helps with liability etc., and so I can imagine it may also make the tax situation simpler if you are based in different countries.

The UK side should be simple, I can't imagine there would be UK tax if work isn't done in the UK, but you should ask a UK accountant about this. The biggest challenge could be obtaining a VAT ID for the company if you need one.

Really you're going about this the wrong way - you have to start with your home country/countries. They're the ones who can make your life difficult.