In short, no. The ways you interact with device nodes are "richer" than what you can do with actual files, and without the kernel on the remote machine having access to your local process memory (which it doesn't, over network), that's not possible.
Not to mention a lot of things you'd want to work with simply have unreasonably high bandwidth requirements (e.g. a high-quality camera in a raw mode), low latency requirements (any USB bulk device that expects something to happen on the computer side within a specified time) or other functional aspects that make operation over the network on a raw device level impossible.
For that reasons, for some device classes, where it is possible to divide what has to be done close to the device and what can be done remotely, there's other approaches: For example, printers can be quite nicely shared via network using CUPS, sound devices using pipewire, jackd or other daemons, video devices using VLC, storage devices either as file systems using NFS, CIFS, … or as block devices (e.g. in Ceph).
Your serial port would be quite easy to abstract - you do the setting up (mostly: opening, setting the baudrate) on the machine where it is, and then just use a minimal network daemon that reads and writes to it.
In fact, that's quite a common pattern, having an UART port somehow addressable over network, in industry automation. Under linux, the
socat programm can do things like that.