The longer you work with Veeam Backup & Replication, the lower and lower its interface work. Apparently, this is because Veeam stores in database information about all sessions of the interface. Once they become so numerous that queries to the database begin to slow down.

So we need:

1. Set up Veeam to not to store all this unneeded information.
2. Delete existing data from database.
3. Truncate and shrink database.

After performing these steps, my Veeam client started to work much faster.