I’m not that versed on all this, but you are correct on both counts. If you use some big box web hosting service it’s likely on aws or something similar, but the alternative is you host your own website. I don’t know if I’d reco hosting it on the same machine your bitcoin is on, but it’s possible. My vision of the future is that we have different network devices that serve as you bitcoin node, you lightning node, you Nostr relay, and then your webhosting for media like pictures and videos.