How do I assign my server IP to a local device?

how can I assign this VPS IP to the raspberry pi or any other local devices?

That's not how the internet works.

In short, the VPS provider has a pool of IPs and it or its ISP is responsible for publishing routes to the rest of the internet, informing the rest of the internet how to route to those IPs.

You can't just "move" the public IP to your local network; the rest of the internet won't route traffic to it. It would be kind of like writing "1600 Pennsylvania avenue" on the front of your house - you wouldn't cause you to get White House mail, right? Because regardless of what you write there, the post office doesn't use it as a source of truth for mail routing.

There's a few of the options you have:

• use ngrok to expose an endpoint to your local service. Ngrok's servers can proxy connections back to your local environment without it having to be online. This will be accessible by anyone on the internet, but is more obscure than an ipv4 address which can and will be easily found (see below). This is a quick and easy solution, and what I'd recommend in your case.

• you already have the VPS. Run the code there instead of on the raspberry pi. It will almost certainly be more reliable and higher speed than your home internet.

• you also already have a public IP, assuming your pi's local router has a route to the internet. the router is performing NAT so that devices "behind" it with only internal addresses can still communicate with the world. You can almost certainly configure your router to forward a certain port to your pi's internal IP address.

• set up a VPN between the private networks, or between the individual hosts on the private networks. This is a lot of work and will require more knowledge of IP networking. If this interested you, I'd recommend looking at Wireguard (recommended) or OpenVPN.

Finally, keep in mind that unless you do something to make it not the case, your service, once on a public IP, will be accessible from the wide world. Since IPv4 space is pretty small by 2022 standards, and there are only 65000 some IP ports per address, it won't take nefarious parts of the internet long to find your service. You can't hide in the obscurity of an IPv4 network.

If your public address is ipv6 instead, those are essentially unguessable and much more likely to go unnoticed. Same thing is true of ngrok - since it has very large set of potential URLs, it's hard to guess. Still, I'd set up some sort of authentication in front of the service. It's just good practice, like locking your house.