MacVim to Skim forward search (without Vim-Latex)

I want to set up forward search from MacVim to Skim. I am using a Mac with Big Sur.

It seems like the problem in forward searching (with respect to backward searching, which is fairly simple to set up), is that one has to tell the editor (MacVim) something about the viewer (Skim), see for example this post.

There seems to be several ways to setup forward search by using Vim-Latex, but this appears overly complicated to me. I am not a fan on the Vim-latex suite, and I prefer to use my own compilation command, which conveniently pops up a terminal window where I can read all errors:

:command Compile terminal ++rows=10 latexmk -pvc -pdf -interaction=nonstopmode -halt-on-error -file-line-error -synctex=1 %:t

Therefore, I am looking for a way to enhance my .vimrc file to perform forward search via the command I just wrote (or a modification of it), without running the Vim-Latex compilation command.

Do you have any clue?

I should add that here there seems to be a solution, but adding that code to my .vimrc does not seem enough (nothing changes when compiling).