Well, now that is really odd because Connections has absolutely zero code in regards to the page set as the site’s home page. The only time I suppose there could possible be an effect is if you have the Directory Home Page to to the same page of the site’s home page. Even then, the only effect should be when following any of the directory related permalinks and would not affect the base permalink at all. If it did, I would expect that would generally break the site.
I guess the path forward would be to login and repeat the same test they did but with one difference. See if it happens with just Yoast and Connections active. Perhaps there could be some weird issue when it is only a combination of plugins being used.