How to use "conda update -n base conda" properly

Question

I have two very simple questions regarding updating conda. I.e. when updating one of my environments with conda update --all, I get a warning

==> WARNING: A newer version of conda exists. <==
  current version: xyz1
  latest version: xyz2

Please update conda by running

    $ conda update -n base conda

My setup comprises a base environment and two actual work environments, say, (env1) and (env2). The latter two environments are kept up to date with conda update --all, issued within each of those environments. The base environment was only generated in the installation process of Anaconda.

Question 1: Should one run conda update -n base conda on the command line of the OS (linux) prior to activating any environment? Or should one activate a particular environment? Or is the environment out of which this command is issued irrelevant?

Question 2: After running conda update -n base conda from out of whatever environment, as determined by the answer to question 1, would a subsequent conda update --all issued within one of my two work environments (env1,2) install or update any additional stuff, only as a consequence of the previous conda update -n base conda?

(PS.: I find many questions on stackoverflow regarding conda update conda, but they don't seem to cover this one.)

Answer 1

If you are very behind on Conda version, updating needs to be done in stages:

For example, to update from conda 4.12 to conda 23.10.0, conda 22.11.1 needs to be installed first:

$ conda install -n base conda=22.11.1
$ conda update conda

Otherwise, by the comment of @merv, it's simply:

$ conda install -n base "conda>$(conda -V | awk '{print $2}')"

which is better than conda update -n base conda, where it might not execute the update.