To go further, you can have a conditional claim like "A implies B", that doesn't beg the question, but in your reasoning for showing why A really does imply B, you can still beg the question (which is what happens in my pythagorean example).

Certain arguments can have premises that do essentially beg the question too though. If I make a conditional claim like "A and B are true therefore B is true", then my conditional claim assumes B is true in the first place. You can't really tell anything about whether or not B is actually true from my claim because my claim assumes B is true from the start.

Just having to assume certain premises isn't inherently logically fallacious. All true conditional claims depend on their premises to guarantee the truth of their conclusion. The issues that can arise with conditional claims are usually that their premises are false or that their premises don't actually imply their conclusion.