It’s hard to say what the problem is, because at least I don’t know your settings.
For example, I saw screenshots (from other users) where Buildings / Zoom Range is [15 - 20], which forces the OSM server to generate a response of about 100 megabytes, and reading data from such a response is also very slow.
I am not saying that this is your case, because I do not know this.
But at the same time, I do not exclude that the problem may be on your side.

OnlineMapsGoogleGeocoding request = new OnlineMapsGoogleGeocoding(search, apiKey);
request.OnComplete += delegate (string s)
{
  request.Send();
};

Fixed:

OnlineMapsGoogleGeocoding request = new OnlineMapsGoogleGeocoding(search, apiKey);
request.OnComplete += delegate (string s)
{
  // Here is the contents of your original delegates, from the script in post # 1.
}
request.Send();

Unfortunately, it’s hard for me to comment on your message about buildings loading speed.
Between Online Maps v3.0 and 3.6, nothing fundamentally changed in building loading.

OnlineMapsGoogleGeocoding.Find(search).OnComplete += delegate ...

to

OnlineMapsGoogleGeocoding request = new OnlineMapsGoogleGeocoding(search, googleApiKey);
request.OnComplete += delegate ... 
request.Send();

In Online Maps v3.0, we marked many APIs obsolete so that all users had time to fix these warnings.
In Online Maps v3.6, we removed the obsolete APIs.

1. OnlineMapsCache.OnStartDownloadTile no longer exists.
Now you do not need to manage OnStartDownloadTile in several places.
Use only OnlineMapsTileManager.OnStartDownloadTile.

2. Use OnlineMapsGoogleGeocoding constructor.
Example:
http://infinity-code.com/atlas/online-m … ample.html

I have upgraded from v3 to newest one and got three errors (two are identical) as follows:

'OnlineMapsCache' does not contain a definition for 'OnStartDownloadTile' and no accessible extension method 'OnStartDownloadTile' accepting a first argument of type 'OnlineMapsCache' could be found (are you missing a using directive or an assembly reference?)

Assets\Infinity Code\Online maps\Examples\Scripts\ExampleGUI.cs(65,44): error CS1503: Argument 1: cannot convert from 'string' to 'OnlineMapsGoogleGeocoding.RequestParams'

Assets\Infinity Code\Online maps\Examples\Scripts\ExampleGUI.cs(86,44): error CS1503: Argument 1: cannot convert from 'string' to 'OnlineMapsGoogleGeocoding.RequestParams'