Red Hat, Ubuntu, etc. are going to support Python 2 for the duration of the operating system releases which shipped it. I would assume that Anaconda, et al. will have similar options for paid customers.
Red Hat has committed to keeping Python 2 on life support until 2024 as part of Red Hat Enterprise Linux 8 [1] so you can get security fixes for Python 2 until then if you use CentOS 8.
Canonical will not provide long term support for Python 2 as part of Ubuntu 20.04 LTS. In Ubuntu 20.04, Python 2 is a "universe" package [2] that does not receive updates by Canonical. This means that the you will only get Python 2 security update guarantees with Ubuntu is on 18.04 LTS until April 2023.
Debian is making an active effort [3] to remove Python 2 and packages that depend on it for its next release. It'll likely support Python 2 as part of Debian Buster until 2024.
Note that if you're reading this to delay your move to Python 3 by another few years, you're doing it wrong. This list shows even all slow enterprise-y distros have a deadline for Python 2, not that you can stretch your stuff for a couple of more years :)
I believe the biggest thing to worry is your application dependencies, if you also depend on packages that come with your system then probably fine (although I noticed that these are largely ignored even if there bugfixes they don't update them)
Otherwise even if your python has security patches for next 4 years, it won't do you any good when you find a bug in one of your dependencies and bugfix is in a version that's python 3 only
Thank you for providing the extra details — I especially agree with your conclusion: go to your boss and say “even if we pay, we're looking at a drop dead date no later than 2024”.
