Update table install process

[WPprodigy]

• Helps resolve an issue noted in Task: Cleanup database installation process #232 where a site has the option set but doesn't actually have the table installed. So instead the is_installed() check now directly checks if the table exists and use the site cache instead of relying just on the option.
• wpmu_new_blog is deprecated, so swapping it out for wp_insert_site.
• Removes some of the direct side-effects from file-loading, and instead more decisively bootstraps the plugin.

Also simplified the usage a bit, now just have the public methods listed below. I checked the methods I removed and didn't see any usage, but because they were public I've added them back with deprecation notices just for extra safety during updates.

is_installed()
install()
maybe_install_during_shutdown()
drop_tables_on_subsite_removal()

The only piece this PR doesn't solve for is the "Prepare for schema changes" action item. Will handle that separately when the time comes, probably with needs_db_update() and maybe_run_database_update() methods.

Testing

Single Site:

1. Setup a fresh single site and check that the table is created.
2. Delete the table manually and flush cache. Reload and see if table is created.

Multisite:

1. Setup a fresh multisite and check that the table is created on the root site.
2. Create a new subsite and check the the table is created.
3. Delete the table on the root site and subsite, flush cache on both. Reload and ensure table was added back.

[WPprodigy]

Did some pretty extensive testing, all looks good.

I like that the install process is rather deterministic. Before it's had the chance to install the custom table, it will carry on and use the the core cron option per a default wp installation. It will install the table on either the installation request (for new subsites for example) or on shutdown of an admin/cli/cron request - but it carries on using the cron option per usual for the whole request if the table wasn't installed yet. Only on the next request does it start using the new tables and our custom functionality - so there is never a scenario where it'll half use cron option and half use the custom table.