In SQL Server Management Studio Object Explorer - How to increase Font Size?
From the tool --> Options --> Fonts & Colors we can change fonts for many windows. T
I had a similar issue where the sql connection box was really tiny. I tried using all the different font sizes for environment but nothing would fix the connection box size. What did fix it was a computer restart. All fonts went back to normal.
You can't change the font of the Object Explorer on it's own but you can change it.