Hi. I was here about something else, but saw your post and last comment.
I think from what you say that you just need to create an account and sign in. Thereafter when you click the iplayer app, you will automatically be prompted to login, without the need to fill in username or password.
I *think* that's the problem from my reading of your post.
How you access the player makes no difference - whether via selecting BBC iPlayer through the link in your box..or using a TV set's built in app button..or a standalone player, like a bluray or 4k player.
It's all the same. The first time you click on it, you will be prompted to login (see my above link), thereafter the process will be the same as described - ie, just click the app and select your account to login without completing any written user password details.