Correction: Ubuntu did ask your permission and you simply missed the fact that VLC and some of its libraries were going to be installed.
This is what you would have seen after typing sudo apt install obs-studio:
Reading package lists... Done
Building dependency tree... Done
Reading state information... Done
The following additional packages will be installed:
libaribb24-0 libavdevice58 libcddb2 libdc1394-25 libdca0 libdvbpsi10 libdvdnav4 libebml5 libfaad2 libixml10 libkate1 liblua5.2-0 libluajit-5.1-2
libluajit-5.1-common libmad0 libmatroska7 libmbedcrypto3 libmbedtls12 libmbedx509-0 libmpcdec6 libobs0 libopenal-data libopenal1 libopenmpt-modplug1
libplacebo72 libproxy-tools libqt5svg5 libqt5x11extras5 libqt5xml5 libresid-builder0c2a libsdl-image1.2 libsdl1.2debian libsdl2-2.0-0 libsidplay2
libsndio7.0 libspatialaudio0 libssh2-1 libupnp13 libva-wayland2 libvlc-bin libvlc5 libvlccore9 libxcb-composite0 obs-plugins vlc vlc-bin vlc-data vlc-l10n
vlc-plugin-access-extra vlc-plugin-base vlc-plugin-notify vlc-plugin-qt vlc-plugin-samba vlc-plugin-skins2 vlc-plugin-video-output vlc-plugin-video-splitter
vlc-plugin-visualization
Suggested packages:
libdvdcss2 libportaudio2 sndiod v4l2loopback-dkms vlc-plugin-fluidsynth vlc-plugin-jack vlc-plugin-svg
The following NEW packages will be installed
libaribb24-0 libavdevice58 libcddb2 libdc1394-25 libdca0 libdvbpsi10 libdvdnav4 libebml5 libfaad2 libixml10 libkate1 liblua5.2-0 libluajit-5.1-2
libluajit-5.1-common libmad0 libmatroska7 libmbedcrypto3 libmbedtls12 libmbedx509-0 libmpcdec6 libobs0 libopenal-data libopenal1 libopenmpt-modplug1
libplacebo72 libproxy-tools libqt5svg5 libqt5x11extras5 libqt5xml5 libresid-builder0c2a libsdl-image1.2 libsdl1.2debian libsdl2-2.0-0 libsidplay2
libsndio7.0 libspatialaudio0 libssh2-1 libupnp13 libva-wayland2 libvlc-bin libvlc5 libvlccore9 libxcb-composite0 obs-plugins obs-studio vlc vlc-bin vlc-data
vlc-l10n vlc-plugin-access-extra vlc-plugin-base vlc-plugin-notify vlc-plugin-qt vlc-plugin-samba vlc-plugin-skins2 vlc-plugin-video-output
vlc-plugin-video-splitter vlc-plugin-visualization
0 to upgrade, 58 to newly install, 0 to remove and 12 not to upgrade.
Need to get 21.0 MB of archives.
After this operation, 98.0 MB of additional disk space will be used.
Do you want to continue? [Y/n]
Note the number of vlc items, and also note the question at the very bottom.
As for whether you installed anything bad, the answer is "no". VLC is a fine tool for watching and/or converting videos.
