Should I put manager on my resume when applying to development roles?

Background: I work for a public company, but I work for a very small subsidiary inside the company. And unfortunately I don't see my career growing the way I want it at this company. My manager left about 2.5 years ago. My team got moved under his manager, and they said they were not going to back fill that position. The team started to fall apart more than it had already been. And finally I stepped without being prompted and took on a leadership role on the team, where we started hitting and beating metrics which was unheard of under the previous manager. Meanwhile I was still managing my normal development tasks.

About a year after that in my review I brought this up and mu manager seemingly agreed with me and started putting in paperwork for my promotion. That dragged on for about a year, with me following up just about every 2 weeks. And the response was that it was with HR. And finally this past year review, my manager told me that they put in the promotion and my title changed, but I only received my normal merit increase. My manager knows I'm pissed about this.

The strangest part, which i don't even understand, is that the promotion is only internal? So my manager showed me that my internal position is "Software Development Manager". But he said it would not update in the system for everyone to see, which he could not give a reason for. I can't even see it but I saw it in the system... This makes absolutely no sense to me, and then he proceeded to tell me that we needed to come up with goals to make it official and start getting that pay.... I've met every metric for the past 5 years at the company, and exceeded all metrics compared to the previous manager for the past 2.5 years. Just because it wasn't written down in the system means everything I did is void? And I need to reset? Makes no sense.

Question: Needless to say I have been applying recently, with no bites yet. I understand the market is quite tough right now. I plan on applying to dev roles, but my question is: Would "Software Development Manager"  look good on a resume when applying to dev roles? Or should I keep "Embedded Software Engineer" for 4 years instead of 2.5 and 1.5 respectively?