Can installed apps be transferred from one iPhone to another iPhone?

transferred directly from iPhone to iPhone, no. But there are definitely ways to get everything from the old phone onto the new phone

Transfer data from your previous iOS or iPadOS device to your new iPhone, iPad, or iPod touch - Apple Support

If there are old apps that are no longer supported, you'd lose those. No way around that.

When you do any of these transfer methods, the apps ultimately just get re-downloaded from the App Store.

Yes and no. You cannot transfer it from one Apple phone to another iPhone that’s not on your Apple ID sign in. If you have two phones under the same Apple ID and you have an iCloud+ account you can share all the apps paid or not to the other phone even if it’s under a separate iCloud Account. Just set it up under your family sharing plan and that’s how I transfer all my apps that I download on one account to my other and it works like a charm. And the added iCloud storage gives you purchases well as had my email private relay chain and quite a few others And they start at $.99 per month