

For your first paragraph: yes, exactly. For software you distribute in binary form to customers, GPL and AGPL are effectively the same thing. For SaaS you can easily use GPL and not share your source code. Though beware if your ever need to deploy your SaaS on the customer’s premises.
The point of these licenses is to not restrict user’s rights, so LGPL doesn’t want you to use their code and not let the user do whatever they want with it according to LGPL. So if I create an app and decide to not maintain it, you’re still able to pull bug fixes etc. even without my involvement.
Yes, GPL effectively makes your binary GPL as well. And if you provide a library for others using GPL code, projects using your library must be GPL-compatible as well.
But the point is that you cannot restrict the user’s rights, so if you distribute the source code you can choose a more permissive license (like MIT) for your code. That could in theory mean that if someone finds a replacement for your GPL dependency and remove it, they could release it under any MIT-compatible license (which is just about anything).
GPL dependencies are often avoided in companies because of its spreading nature where it makes everything it touches effectively GPL. And even if you write SaaS, if you’re B2B you’ll eventually land a bigger customer with strict software policies and you’ll have to deploy on customer’s servers, thus having to legally distribute the source code as well.
You don’t have to provide it automatically, but shall they ask for it, you have to deliver. And relying on the customer never asking is not the best business decision. See for example here: https://boehs.org/node/truth-social
Yep.