Okay, I see the reason. It turns out, PHP 7.4 no longer bundles a (newer) private copy of libsqlite3 (see https://www.php.net/manual/en/ref.pdo-sqlite.php, https://www.php.net/ChangeLog-7.php#PHP_7_4, https://www.php.net/manual/en/migration74.other-changes.php).
So now the default build configuration (which is what Travis provides) is built against whatever version the distro supplies – which for Ubuntu are the aforementioned versions.
So you’ll need to work with PHP developers to figure out if it’s possible and how to hook 7.4 to a newer private copy of libsqlite3 – as it was their decision to change the software’s scope of supply.
It’s up to Travis staff whether to implement the result as the default, but you can always build a custom PHP version from source and use that.