The only thing you're doing wrong is expecting your Roku to save all of your logins for every single app you installed. That's not how it works.
Apps that do their billing through your Roku account (the apps you did not have to sign back into when you bought another Roku device), are the same apps that will show up in your Roku account when you sign in through a computer or mobile device at roku.com. Anything you see under your account at roku.com under "subscriptions" you should not have to sign into on a new device provided you have already entered your Roku credentials. Anything that does NOT show up in your Roku account you will absolutely have to sign into again. Also, if you have any apps such as nbc, cbs, abc, History, AMC etc. that you used to watch over a cable or satellite service (Comcast/Xfinity, Dish etc. that you still subscribe to), you will have to authorize those apps through your subscription service.
Apps like Netflix, HBO, Showtime, Starz, etc. you will have to sign into individually. They are services independent of your Roku account and your subscription service through a "traditional" cable or satellite provider.
To make things even more confusing, many of these streaming providers are now offering bundles. For example, I get Showtime, but not with the Showtime app. I already had Paramount Premium, then they started offering Showtime within the Paramount app under the same login I use for Paramount. It was only a couple of bucks more so of course I went for it. Many streaming providers are offering similar bundles that only require you sign into one app to watch two services. Chances are you'll have to sign into those separately from your Roku sign in as well.
In short, you're not "doing" anything wrong, you're just lacking some understanding of what's included with your Roku sign in and what is not.
onn Roku 43" TV model 100012584 running version 12.0.0
Twenty plus years of online experience as a web developer, general user and consumer. Recording engineer. Sixty plus years of troubleshooting and problem solving in several fields. Here to help and get help when I have issues with Roku. Nothing more. Not here to socialize. That's what real life is for. 😉