I am using a package that has received an update on CTAN yesterday (3rd of June 2021). I wanted to download the most recent version of this package via MiKTeX console, but according to MiKTeX console, no update is available. I am curious how long it usually takes for updates on CTAN to become available on the download mirrors that MiKTeX relies on. Should I expect hours, days, weeks or even longer time periods here?
Usually you will have to wait a few days.
While TeX Live (usually) pulls updates from CTAN daily, MikTeX does so slightly less regularly every few days (about 3 to 10 days). It is not unusual to have to wait for a week, but usually it does not take much longer than a week and a few days.
As a data point there were updates on 2021-06-03, 2021-05-29, 2021-05-20, 2021-05-18, 2021-05-09, 2021-05-08, 2021-04-27, 2021-04-23, 2021-04-14, 2021-04-07.
Once MikTeX has packaged the updates, it takes a while for all mirrors to pick up the changes, but there we are usually talking hours.