The most common seems to be auto-deployed to staging or a dev environment, with some sort of daily or weekly process for promoting to production. One company built a Slack-based approval process using +1 or -1 reactions, and another has a zoom meeting where every author has to attend and is walked through a checklist before the release is approved.
My team also had a manual approval step to production, which theoretically meant the dev would check logs, dashboards, and alerts before approving, but in practice both with us and teams I talked to, that is followed about 50%-80% of the time.
What we built into our product, Sleuth [1], is a way to automatically promote staging releases when the staging release was determined to be healthy and soaked for a minimum amount of time. This allows the 80% case to simply flow through to prod without developer babysitting, whereas we can easily interrupt the process with a -1 reaction in Slack if it needs more manual testing. I think this is the ideal - the common case is the code flows but you still have an easy way to interrupt the process when the change needs it.