tl;dr Thanks to @GaryPendergast I now switched from latin1 to utf8mb4.
Well f*ck me but I really didn’t take care about my blog at all any more. Checked the logs and an occasional error about emojis and the database showed up. On investigation I found out that the database was still running on MYISAM and latin1. WordPress never updated this during upgrade (despite my DB having support for this for ages). My website moved a lot and existed even before switching to WordPress in 2004 so it’s sort of a miracle that it’s still working anyway. Unlike Geocities and the likes I mean 😉
PHP message: WordPress database error Illegal mix of collations (latin1_swedish_ci,IMPLICIT) and (utf8mb4_unicode_ci,COERCIBLE) for operation [...]
Fixed by running this SQL on all of my tables:
ALTER TABLE wp_posts ENGINE=InnoDB ROW_FORMAT=DYNAMIC;
ALTER TABLE wp_posts CONVERT TO CHARACTER SET utf8mb4 COLLATE utf8mb4_unicode_ci;