inside one file, I have difficulties going quickly up function by function
helm-occur
Just start typing and it will show you occurrences in a file; you can use C-n/C-p (or whatever you bind it to), and it will move the point in the buffer and show you the occurrence so you can see the surrounding text. If you C-g the point is left where you were, and if you just press enter your point will be placed at the occurence.
If you use Magit, LSP and Projectile to code Rust, have you tried to clone the repo(s) you are working on to your local computer and enable git server on remote so you can push your changes. Or if you don't wish to enable git server, transfer files from the work machine to remote via some other means (sftp) and just commit when you know you are done. It would remove the latency for the most part. Otherwise you are perhaps better off running Emacs on the remote and forward X to your work station, have you tried? Or probably even faster, just ssh into remote and run Emacs in terminal.
I am not sure if it is tramp problem; it is probably that you are just generating too much traffic if you are using Emacs on a remote as if you would be using it on your workstation.
It is painfully hard for a new user to start out on GNU Emacs and get everything they want running and if they are not patient, they will outright quit.
I don't know man; I started some 20+ years ago with vanilla and for the first like almost 20 years I had no more than perhaps 20 - 30 lines of elisp in my .emacs file.
I used it so until some ~3 - 4 years ago when I got more interested in Emacs and started to learn Elisp and tinker around with it.
helm-occur
Just start typing and it will show you occurrences in a file; you can use C-n/C-p (or whatever you bind it to), and it will move the point in the buffer and show you the occurrence so you can see the surrounding text. If you C-g the point is left where you were, and if you just press enter your point will be placed at the occurence.