Hi AL
Sounds like almost recreational. I wish I had that many RPi. I have a couple of them but of different models. Why RPi 3 (Model B or Model B+)? Considering the true network bandwidth, I think RPi 4 Model B is the sweet spot for a web server, especially a cluster. Well, they are also much more expensive.
About the different Moodle versions, each of the five web servers run a Moodle 4.5 LTS, 5.0 and 5.1? So, through the HAProxy one sees three Moodle sites: a 4.5 LTS, 5.0 and 5.1?
The transition to HTTPS could get tough sometimes. The first thing, your cluster must be in your private LAN. How did you get the SSL certificates, the "Snake oil" ones in Apache? Did you match the timing of the Apache reconfig and Moodle wwwroot? Apache restarted? Have you set up a redirection HTTP to HTTPS? I could imagine the server cache in a RPi mounted file system being sticky. Those two are the most common causes of too many redirections. In the worst case try from a different machine. In the worst case, you have to start with a single web server. Once that works switch on the others.
And how do you off-load the HTTPS part, does the HAProxy handles it (better) or delegated to the web servers? Did you play with $CFG->reverseproxy and $CFG->sslproxy?
That said, why HTTPS in a private LAN needs some explanation too.
P.S. This is entirely different from the "Composer vendor" story, so I took the liberty of changing the subject line.