I use docker + traefik + a simple domain alias in my router to give all of my services easy to remember dns names.

Unbound is a recursive DNS, not an authorative. An authorative DNS server is needed for adding your own records. I suggest using bind, which can be both a recursive and an authorative.

This is very unlikely, but does your ISP router offer any dynamic DNS options with the DHCP?
The process would be DHCP giving out address --> Host registered, returns Hostname --> DHCP gets hostname --> DDNS update sent to DNS server

I do a few things to keep track of my installed services.

1. I run an instance of Heimdall, which is an utterly simple launcher. All of my services with administration panels get added here.
2. I maintain an excel sheet with all of my assigned IPs. It doesn't matter if it's a VM, a container, an iPhone, or some other hardware device. Everything is assigned a static IP and added to the excel list.
3. When I'm creating containers and VMs in Proxmox, I make sure that the proxmox ID of the container or VM is the same as the final octet of the IPV4 IP address. So if my Heimdall service is set up on 192.168.1.155, then the Heimdall LXC gets ID 155. I do this so that I can quickly look up the IP of any service in Proxmox without having to open my spreadsheet.

If you follow this convention, then you could easily export the IDs of all of your proxmox containers and VMs by following the instructions here. Make a few transformations to turn the IDs into IP addresses, and you have a .csv you could import elsewhere.

I'm sure someone has made a tool to do this already somewhere. On Github, xezpeleta made an inventory script "to grab proxmox nodes. This will also try to grab the IP if you have the guest agent installed." I bet there are others out there.

I‘m not sure if I understand your problem. How many VMs, hostnames, etc. are we talking about?

Can you put your own router behind, what I presume, is the ISP router? Then you can manage DHCP and IP address reservation.