The python3-pip package installs /usr/bin/pip3, so simply invoke it as pip3, and not pip.
That of course, means you're going to use Python 3 version.
For Python 2 version, install python2-pip and launch it as either pip2, or simply pip.
I hope it's needless to say that you shouldn't be later using pip as root, as this is going to ruin your system sooner or later. Set up a virtualenv and use pip there.
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You are doing nothing wrong, 8.1.2 is the newest version of pip available in the EPEL 7 repo. RHEL/CentOS 7 usually doesn't get new versions of software, only bugfixes, and same applies to EPEL. There are some CVE fixes and other recent patches in the pip EPEL repo so I'd assume it's being actively maintained and safe to use.
8.1.2 is the latest version that's available in the RHEL repos for RHEL 7.6 (and also RHEL 7.8) for the corresponding version of Python which is 2.7. Version 19.3.1 is available but it's for Python 3.8. You can see it available if you enable the necessary RHEL repos and search for the package with yum:
subscription-manager repos enable rhel*
yum list available | grep python-pip
That will show you the latest versions for all of the available versions of Python including 8.1.2 for Python 2.7 and 19.3.1 for Python 3.8.
If you want version 21.x, then you need to install a later version of Python such as 3.8. Python 2.7 is no longer supported and won't receive anymore updates.