If you are looking for what the vast majority of churches do, they are overwhelmingly under 300 members and if they have a website on a CMS then it’s usually Wordpress (I’ve seen many on Squarespace, Weebly, or other builders too). At that size they usually only post their sermons once a week, if at all, so they spend a few hours on it. Some are on a hosted or high-performance stack, in those instances the outsourced company usually only provides technical support and hosting but they may provide a certain amount of updates. I saw a lot of predatory rates being charged for basic websites so I eventually built a Wordpress hosting solution with a curated set of plugins and a popular theme with a builder (Divi) that we let those small churches and missions organizations in our region on pro bono.
Now, when I’ve worked in very large/mega churches, there tends to be dedicated resources in the communications department to web development/upkeep. They may outsource design, but communications handles weekly updates, sermons, etc.They’ll usually work with media/worship arts teams so they do draw some man hours from there as well. If IT is involved then it’s strictly hosting/stack and possibly custom php development. I haven’t worked in anything bigger than 10K so things may swing beyond that size, but the above is what I see 99% of the time.