Hello again!
There are a lot of issues with the subdirectory settings of Polylang and the homepage, all of which are out of our control. You’ll be facing these issues with all SEO plugins because Polylang doesn’t send the correct information to WordPress; at least, not as early as it should. I have tried fixing these issues via The SEO Framework, only to find the modifications breaking after a few Polylang updates. The monkey-patches in Polylang brought specifically for other SEO plugins will break things as well–this is too complex to comprehend.
There’s an active issue running here for the homepage canonical URL:
https://github.com/sybrew/the-seo-framework/issues/325
As for the homepage titles, I suggest emptying all fields in the global Homepage SEO Settings meta box and supplying the data via the homepage edit screens instead. You might want to provide a canonical URL there, too; this might solve the issue.
I also suggest setting up the plugin to translate via subdomains, as it’s a little more consistent. It will require you to set up some subdomain DNS values.
The correct approach:
Now, the solution is abiding by the WordPress API — which no traditional translation plugin can inherently do: WordPress must be hijacked to provide such translation support. The only correct approach is using WordPress’ multisite, where you set each subsite to a specific language, which is used exemplarily by (es.)WordPress.com and (es.)www.remarpro.com. This approach is further supported by MultilingualPress.
I hope this helps! Cheers ??