When I'm in "the loop" (archive pages etc.) how do I force teasers / excerpts for all articles, regardless of whether they contain the `<!--more-->` tag or not?

Details:

I'm starting off of the `_s` template which displays blog post content using [the `content.php` template](https://github.com/Automattic/_s/blob/master/content.php#L21) in which it calls `the_content()` function. This function inspects the post and tries to find the `<!--more-->` tag in. If it finds one, it returns a teaser and a *read more* link, if it doesn't it simply outputs the whole post.

I'd like to keep the first part, i.e. respect the `<!--more-->` tag if the content author used it, but if he/she forgot it I want to automatically display the teaser / excerpt anyway (something like the first paragraph or two).

What is the best way to do this? There is [a `the_content` filter](https://developer.wordpress.org/reference/hooks/the_content/) but e.g. the read more customization text doesn't come into it. What would you recommend?