Steven Zahm@ Sergio
Sorry, but I fear the web host is misleading you. There is no deprecated code in these places.
For example, here is the documentation for the ob_get_clean() PHP function. If it were deprecated there would be large warning indicating as such. Here is an example call_user_method().
And… the class.entry-object-collection class is brand new, just introduced in Connections this year and is modern.
In fact, a function being deprecated is not a bad thing. It is merely to let developers know that at some future point it will be removed. The whole point is to allow developers time to migrate code and release updates well in advance of a function being removed.
Now, back to the Fatal error: Out of memory error…
This is PHP telling you the memory allocated to PHP has been exhausted. Why the host is claiming deprecated code is puzzling since the error is very specific. Here’s a link to a tutorial how how to increase the memory allocated to PHP.
Just as important… learn which version of PHP the host is using to run your site. WordPress recommends version 7.1 because it runs WP much faster while being far more resource efficient. Many web hosts allow you to chose the version to run from right within their control panel. I would check there first and if you can not find it, ask their support channel.
Question… which site/page are you receiving this error message? If it is the site’s frontend directory. The page where you inserted the [connections] shortcode. If you are displaying many entries, let’s say more than a hundred. It is possible to get that error. If that is the case, you need a template which supports pagination. By default, they limit the display to 20 entries per page. This is for optimal performance and resource usage. This is not a Connections bug or limitation, There same would occur if you were to try to display that many WP posts on a single page.
Hope this helps!