Separation Anxiety Tips, cries when I actually leave but is fine by herself while at home

I know this is probably the millionth post about cavapoo's and SA, but I'm so conflicted because I thought my girl didn't have SA. From the third day we got her at 9 weeks, she's been crate trained & will sleep in it with no problem since I have forced naps since we got her. Got her a playpen a month ago and she's fine playing by herself while we're in our room. Like she keeps herself entertained, but the moment I pretend to go out the door, she starts crying, even though she can be left alone while she's in her playpen and crate while we're home. We mainly keep her in the playpen so she doesn't follow us 24/7. Also her playpen is "attached" to her crate so she'll go in and out. She's just turned 5 months, and today was so bad. I had to leave to go to the grocery store, and while I was getting ready she cried, and then was even louder the moment I stepped out. It was so bad how she was crying/high pitched barking I had to go back in and give her puppy melatonin. I've been "training" her I guess for the past week to get her used to hearing the door close and she'll cry instantly.

People say let the puppy cry it out, some say it causes them to stress and it's not good for them. I let her hear keys jingle, me put on my coat/shoes & walk around in it, and fake leave. One day while doing this she cried for 5 seconds then went back to her toys but that was only once. I know she's still a baby, but her crying while I'm gone while living in an apartment is so frustrating. Are there any tips? Do I just keep fake leaving and hope it gets better?

I do plan on getting a dog camera because I don't think she cries the whole time.

Also to note, I am thinking I didn't tire her out long enough because I have left before while she was asleep and heard no crying when I stepped out, but I don't want tiring her out to be the end all be all? I want her to be okay with us leaving while wide awake.

Also, in general whenever my partner or I come back home whether it's both of us coming back, or one of us we never greet her instantly and ignore her if she's jumping on us and only greet her when she sits down. Maybe I am expecting too much, but I just want my pup to be trained well, which is why we start the 18 week training Jan 1st.