Website blank (not redirected properly) if I activate SSL

Hello,

I’m transitioning the websites I host to their SSL versions, and I’m stuck with one of them.
First things first, I apologize, I can’t share its URL, I realize it’s not going to help.

Once I do the requirect actions to transition the website to https, the administration of the blog is dead, the admin pages are purely impossible to load, the browser telling it it won’t work, something isn’t redirected properly, etcetera (the exact error message depending on the browser, but you’ll have recognized it by now, Chrome: Err_too_many_redirects), and the public face of the website has the same problem

Could I humbly ask you for help in this regard? I don’t know where to look at this point.

More details follow ??
Let’s make it in the form of a bullet list, it’s long, but I didn’t want to leave anything:

? Double-checking: the website’s SSL certificate has been properly installed.
I’ve transitioned 4 other wordpress websites to SSL before this one, without problem, so I’ve got it working now. Let’s Encrypt is installed on the web panel, auto-installed and auto-configured, all good. The other wordpress websites I transitioned work well without issues too.

? Double-checking: non-dynamic contents work. I can load images inside the blog’s wp-uploads directory by typing their URL in the browser, with either https:// or https:// , it will work, so these are clearly the dynamic contents that cause a problem.

? Confirming: both the admin and the public version of the site are affected, too many redirects, content not loaded, depending on the browser it’s a different message, but it’s the same error

? The ways I tried to transition the website to https? Two ways, both of them explained on the guide I used as reference: https://www.wpbeginner.com/wp-tutorials/how-to-add-ssl-and-https-in-wordpress/

. First in Admin > Settings > WordPress Address (URL) and Site Address (URL), add the little “s” after http, and then update the .htaccess (I’m with Apache, LAMP) with that snippet: `<IfModule mod_rewrite.c>
RewriteEngine On
RewriteCond %{HTTPS} off
RewriteRule ^(.*)$ https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
</IfModule>`

. Second, by installing the Really Simple SSL wordpress plugin, https://www.ads-software.com/plugins/really-simple-ssl/ . I installed and activated it, it told me the job was done, and next thing you know, problem.
A slightly different problem: the blog admin pages are dead, but the public face of the website still works… although it’s still in https://www. and not in https, and loading by force an https version results in an automated redirection to the non-ssl version.

? How I restored the blog after seeing the problem, between each attempt: I had to go into PhpMyAdmin and manually edit the siteurl and home fields in wp_options to remove that “s”, for the site to work again

? The little detail I noticed: no need for the .htaccess snippet editing, simply changing https:// to https:// in the siteurl field, WordPress Address (URL) in the blog admin > settings page, is enough to trigger the problem.

? Double-checking: might it be a cache getting in the way? The website is behind Cloudflare and has the wp-supercache plugin. I placed Cloudflare in development mode (they stop caching), purged the cache of Cloudflare and wp-supercache, deactivated wp-supercache, waited 5 minutes, and tried again: same problem.

? A possibility: might it be caused by a bad .htaccess? Maybe. It is a very cluttered file, see, I uploaded it to Pastebin: https://pastebin.com/RnbqZbCF
But I had the problem again after I stripped down the .htacess to its bare basics,

# Added for SSL, ref https://www.wpbeginner.com/wp-tutorials/how-to-add-ssl-and-https-in-wordpress/
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteCond %{HTTPS} off
RewriteRule ^(.*)$ https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
</IfModule>

# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>

# END WordPress

I even tried without the last paragraph (which killed the fancy URLs in the public version of the site, before I applied the https to the site URL in the admin settings), but that didn’t help at all either, same problem.

…
And this is it, as things are, I reached the end of my wits, I have no single clue what I’m doing wrong (I’m not blaming the software).

Please, would a kind soul have an idea, a suggestion, a hint? Or, miraculously, the solution?

Thank you very much if you can help ??