nvim-config-local VS confiture.nvim

it's been undeprecated recently, but if you would prefer to use a plugin, I use this one

The next version of neovim (and currently, nightly) re-enables support for exec, which sounds close to what you want. In the meantime check out https://github.com/klen/nvim-config-local. These both do a single file, but once you're running some code it's easy enough to get that file to source more.

I just use nvim-config-local, which is basically just souped up :h 'exrc'. And then from there I typically set makeprg and a custom "run" command if I want, along with any other settings I might want in the project. I tried using some custom runner type plugins in the past but I think this method has provided me with the most flexibility, and I don't have to learn anything new because it's just the same as what i do in my init.lua.

I took inspiration from nvim-config-local and added an integrity check, to force the user to review the settings file at least once. It's on by default, but is optional. The file can be safe to use if you don't expose any option that allows for arbitrary code execution.

nvim-config-local

This is also not a direct response to your question as I'm not familiar with asycntasks.nvim, but having a build and run functionality is probably the main reason why I wrote confiture.nvim, which is another task launcher plugin (that also aims at being simpler than overseer). The main limitation with the implementation of the build and run of confiture is that the build phase will not be asynchronous. It is sufficient for my workflow though -- if I know the build command will be long, I usually launch it on its own first, which can be asynchronous using confiture (with vim-dispatch under the hood).

It's can also be used from vim to launch custom commands (as is done for example in my other plugin confiture.nvim)

It doesn't answer your question but this is how I do what you described : https://github.com/romainchapou/confiture.nvim

I'm mostly fine with language specific configuration, which I find not too hard to manage in my init.vim, but I rely a lot on project specific commands for building and running projects, so I'll do a shameless plug for my plugin, confiture.nvim, which aims to provide a simple solution for this.