You can look at it this way. That piece of paper that says he adopted you doesn't tie you to him any more than my DNA ties me to my biological parents. We are who we choose to be regardless of who we're connected to, or how we're connected.
I didn't adopt my stepdaughter (and I only ever use that term when it's necessary for clarification, like now), and I'm the only father she has ever known, and I consider her my daughter just the same as all the rest. And she considers me to be her father, regardless of DNA. I'm her dad, and she's my daughter, and it's just that simple. It's a bond forged out of love and caring, and genes or a piece of paper wouldn't make it any stronger.
And as to the last paragraph I agree and salute you sir.
In my situation I came with the package. Born out of wedlock in 1950. That was a serious in that time. I was the oldest of 5 kids and noticed very early that they were very different from me. My step dads relatives treated me almost with distain and the ones that did care still treated me differently. So when my Mom finally broke down and filled me in at the ripe young age of 14 it became pretty clear to me why. But I was made promise not to tell anyone our secret. Kind of idiotic as my siblings were the only ones that did not know. Step dad was nowhere to be found for that conversation. You said love and caring. Nope. NADA. No real bond was ever established.
I had to wait until my Mother passed to get my real birth certificate. She refused to share that info with me. Told my spouse it was none of my business. I had to near threaten step dad to get the papers. And he was pissed about it. Some people just basically suck.
I did find my birth father but never met him. Never cared to actually.