Hi,
With current master (8785ea0) I made some tests on a MySQL 5.5.37 server containing about 81000 databases and about 81000 users.
In the mysql.db tables there are about 81000 grant entries; each one grants some wildcard access to databases starting with a certain pattern.
I tested with root, since the reports we got about the server being slow seem to be occurring for root.
Good news ---------
First, the login. It takes about 7 seconds before seeing the initial page after login.
In the navi panel, there is a db page selector with 107 page numbers. Going to any page takes about 7 seconds. Opening a db takes about 4 second (each db seems to contain about 31 tables).
Browsing tables, grid editing, searching inside a table behave normally.
Using Server > Databases works correctly, including switching pages.
Problems --------
Going to a MyISAM table, Structure, and trying to change a column's structure takes 30 seconds before seeing the dialog for this column. Switching this table to InnoDB does not help.
Database filter: I got mixed results. Sometimes it works (after about 10 seconds) but sometimes it stalls and does not find anything. I could not find a consistent way to reproduce.
Server > Users: "Error in processing request. Error code: 500. Error text: Internal server error".