Both Ken and Howard are (in my opinion) technical experts when it comes to servers and moodle, really great guys to have around. I am still a somewhat novice, so I will attempt to give you my simple explanation of what is going on.
Somewhere along the way (I can remember exactly at which Moodle version number), Moodle started liking both utf8mb4_unicode_ci and Barracuda. So it was highly recommended that one transition the MySQL database to these “future” requirements. As I recall, the Barracuda move became troublesome for “hosted” servers because Barracuda required a modification to the database, and this change was more than what most low-cost hosting products wanted to support. Then, maybe in Moodle 3.4 or so, utf8mb4_unicode_ci and Barracuda became a requirement. Maybe technical experts can figure out how to avoid it, but common folks like myself could not. As another example of transitions, in Moodle 3.5 you needed php7, period. Oh, maybe technical experts can figure out how to avoid this, but common folks like myself can’t.
I am not sure who discovered it, maybe a fellow named Usman (another great guy), but there was a somewhat backdoor approach to not needing utf8mb4_unicode_ci (and maybe Barracuda) which involved installing an earlier version of Moodle (maybe 3.2 or something like that) and then upgrading it to 3.4. My sense is that this is what Bluehost did, with success. I am not sure if this backdoor approach works with Moodle 3.5.
But what I read in your posts is that you really want to run the latest Moodle, even willing to install it from scratch, and probably will want to continue upgrading it. So, until server companies like Bluehost move to Barracuda, you are kind of stuck if you want to run Moodle on low-cost hosted server.
I see two options for you if my understanding of your desire is correct. 1) Find a low-cost server company that does support Barracuda, or 2) Get yourself a low-cost VPS. The bad news is that a low-cost VPS is probably 5 times more expensive, typically starting around $25/month, compared to $5/month for a hosted server. The good news is that you will have much more control over your database and your whole server. Also, you will get better performance from a VPS. Running my Moodle on a VPS is my current solution. I run my Moodle on a (mid-cost) VPS. My Moodle supports around 500-600 students per year, around a dozen courses a year… no problem. I am not sure about your needs, but there are some logical steps (hosted to VPS to Dedicated, for example.)
There remains some more bad news about a VPS. Many server companies provide less (free) support for VPSs, they expect you to know more. But if you can install Moodle from scratch, you might be the kind of person who will have success. I am a professor, not a server-guy. I enjoy learning, and I have had very good success with VPSs for the last six years. And with folks like Howard, Ken, Usman, and many other great people here on Moodle.org, they are around to help me when needed.
Incidentally, you might know this, but Barracuda is not a separate product. It is (in my simple terms) telling MySQL to be a different “sex.” So one often does this by editing a my.cnf (MySQL) configuration file. This utf8mb4_unicode_ci stuff is like telling MySQL to speak a different (and better) language. One can do this utf8mb4_unicode_ci stuff in a variety of ways, but I do it when I create my MySQL database, and I also reinforce it in my my.cnf configuration file (probably a redundancy, but I do it anyway.)
Moodle can be run with a variety of different database products. I ran MySQL forever until this year when I decided to try MariaDB. So far, so good.
Why isn't some of this in the docs? Someone has to decide what is absolute and not absolute, and it is kind of like "Where do we tell people the various php extensions that are required, like intl?" The best way to do this, as you have found out, is to read the docs and then ask questions here on Moodle.org.
So, if what I have said is helpful, great. Both Ken and Howard will probably add to what I have said and provide some technical corrections and more great advice.