These pathes don’t belong in your build.zig.zon, the pathes within build.zig.zon should all be relative pathes that are subdirectories of your project folder and they are for files that you ship with your project, if you wanted to ship certain build libraries as binary files with your project you would have to copy them to a subdirectory of your project, but it would be better to instead allow the user to specify the include path for the system library (or create a package that build the library from source).
If you use zig build-exe you can use -L/usr/local/mariadb-10.3.37-linux-systemd-x86_64/lib -L/usr/includes/mysql -l<name of lib without extension>
If you use build.zig and zig build you can use zig build --help to see this:
...
System Integration Options:
--search-prefix [path] Add a path to look for binaries, libraries, headers
...
I haven’t worked with zig and mysql in combination.
But you should try if this example works for you: