Moodle is the heaviest ordinary web application most organisations will ever run, and its requirements keep climbing. Moodle 5.2 asks for a minimum of PHP 8.3 with 8.4 supported, 64-bit PHP only, the sodium extension present and max_input_vars at 5000 or above. The database floor moved too: PostgreSQL 16, MySQL 8.4, MariaDB 10.11. Check that last one on any shared platform before you plan an upgrade, because a database server one minor version behind is a hard stop rather than a slow site.
Cron is not optional and web cron is deprecated, so command-line cron every minute is the only sensible setup. The load pattern is the other thing to understand. Moodle idles cheaply then spikes hard, and the spike is almost always a quiz: thirty learners starting a timed assessment together will do more to a server than a thousand people reading course pages across an afternoon.
FormaLMS is alive but conservative, and its own documentation still specifies PHP 8.0 to 8.1, both past end of life. Confirm current compatibility before committing. Xerte is actively developed and undemanding, which follows from it being an authoring tool rather than a platform under load.
Not for you if you run timed high-stakes exams for hundreds of simultaneous candidates. That needs dedicated resources, and shared hosting is the wrong shape for it whatever the plan says.