How to make dependency auto-install in pyproject.toml?

Question

Description

I have new Python project containing 1 package with 1 dependency. I uploaded the package to PyPI (test) and when trying to install it using pip I get errors. However, if I install the package on which the project is depending I can install my package without issues.

pyproject.toml

[build-system]
requires = ["setuptools >= 61.0"]
build-backend = "setuptools.build_meta"

[project]
name = "mediagrab"
version = "0.1.0"
authors = [{ name = "mrprikol", email = "prikolus@proton.me" }]
description = "Python CLI for downloading videos from YouTube"
readme = "README.md"
requires-python = ">=3.11"
dependencies = ["pytube==15.0"]
classifiers = [
    "Programming Language :: Python :: 3",
    "License :: OSI Approved :: MIT License",
    "Operating System :: OS Independent",
]
license = { file = "LICENSE" }
keywords = ["python", "cli"]

[project.urls]
Repository = "https://github.com/mrprikol/mediagrab"

[project.scripts]
mediagrab = "mediagrab.__main__:main"

Command that I use to download my package: pip install -i https://test.pypi.org/simple/mediagrab

My goal is to have ability to install the package without installing the dependencies manually. How can I achieve it?