Include more of your dependencies in the repo and build them aa part of the ordinary build process. Now a package manager does not need to get involved.
Manually copy-pasting source trees around sounds like such an outdated idea from decades ago on how to approach dependency management in a modern programming language. Not to mention that you then have to hook them up to the build system that you are using and not all of them will work out of the box with the one you are using for your project, sure, if you are using CMake and your dependency uses CMake, you can add a subproject, how do you deal with it when they're mixed-and-matched aside from rewriting the builds for every dependency you're pulling in; or without manually writing glue shell scripts to build them independently and put them into a directory? How do you then ensure the said shell script works across different platforms? There are way too many issues with that approach that are solved in other languages through a standardized project management tool.
You don't have to actually copypaste. You can use CMake and FetchContent/CPM. You can specify custom build commands or inline declare a project for anything small that you pull in that doesn't use CMake (you can call add_library with a glob on the folder FetchContent pulled in, for example - I've done so here https://github.com/basis-robotics/basis/blob/main/cpp/CMakeL... for a header only lib). For large external dependencies that are either very slow to compile or for some reason aren't CMake, reach for the system package manager or similar. If you want to be really cross platform and are supporting Qt/wxwidgets/etc, vcpkg+CMake+clang is solid combo, if a bit slow and a bit disk space heavy with the build cache.
And yet that's the right approach. It's not really copying but rather onboarding.
You don't want to depend on a third-party hosting the code, so you need to copy it, and pin it to a specific version. You might also need to patch it since you'll be using it and most likely will run into problems with it.
Using third-party code means taking ownership of all the problems one might encounter when trying to use it in your project, so you might as well just adapt it for it to work with your tools and processes.
If you use a modular system this is essentially just maintaining a fork.
Have you taken a look at CPM ? https://github.com/cpm-cmake/CPM.cmake . It makes CMake project management easy - no need for separate package manager tool.
That’s similar to what vcpkg does under the covers. It clones the repo containing the dependency’s source code and then compiles it using the same compiler as the rest of your project. This avoids static libraries and ABI considerations while also avoiding having to copy/paste their entire source tree into your own.