Just glancing back and it sounds like you've had some changes (newly wed in 2018) so that can be a lot for a little person. Your new husband just was in ICU - scary and hectic - for a seven year old too.
Seven is a big leap in kid maturity levels - a counselor once told me that. If she's had changes, her maturity will be on the low side possibly, and she might just be a bit behind. Sometimes kids that age can't handle their emotions as well as we'd expect and that's ok.
I wouldn't say Don't be sad. Imagine if you felt a sense of loss, and someone said that to you. She might not get the difference between 'miss' and feeling 'sad'. She should know it's just ok to feel as she does, and that she can let it out.
You say you're run off your feet. You mentioned your husband doesn't pull his weight with his kids every 2nd weekend, and that you are pressed for time. How about making a girl night for you and your little one - have a sleepover night for she and you in your bed, or movie night or whatever - just you two. I did that with mine when they were upset. Really helped.
Have her enjoy/engage in activities she enjoys with kiddos she has fun with and has opportunity to meet new ones. Then go and watch her when you can. She just needs you to give her that attention. Sometimes the youngest ones miss out - especially when the older ones are teens.
It's not always what you think is causing it (the sadness) - it's just a symptom of a bigger issue. She might just be feeling a little lost and neglected. A lot of changes and that's a big milestone year for kids - emotionally (maturity wise).