When you buy a domain name, DNS is just a way to link that name to your IP.
When your IP changes, you need to notify the DNS servers that it has changed.
In the real world, DNS would be a book where people's names are written alongside their house address. If you change house, you need to tell the editors of those books your new address.
Dynamic DNS providers are like normal providers except that they continuously edit new versions of their book and make it easy for just anyone to update their address automatically.
Given what you say though, I would not proceed like that. Either just get a cheap VPS as a fixed-IP bridge or use something like Tailscale to manage the dynamic side for you.
I say this because dynamic DNS services can be a bit problematic at times. If you change IPs like once a week/month, it's absolutely fine though long-term SMB/NFS shares will fail very badly when that happens. If you change IP for every GB downloaded, that will be a real pain real quick (IP update is far from instant when going through DNS).
You'll learn more about routing with the bride setup but you'll get a much nicer 'turn key' experience with Tailscale, wherever you are. With both solutions, long-term connections won't be a problem: the only downtime you'll get is where either one of your box actually restarts.
::1.