How to get this visual effect on typeface?

Gaussian blur makes the effect partially. But it doesn't make the foggy bridges between the parts as you seemingly have noticed. Here's a slightly more developed attempt:

In the bottom there's the background layer

In the middle there's a text. It's rasterized for free adjustments and effects. It has got a slight gaussian blur and another filtering Noise > Median. Median filtering finds what's around a pixel and takes the most common color. It tightens blur at the edges and generates those foggy bridges.

Median spoils the definition of the letters if it has large enough radius to make bridges. The definition is partially restored by inserting a copy of non-blurred text to the top layer. It has reduced opacity to keep the appearance still blurry.

The opacity reduction explains the transparency of word "To" in your example.

You are correct-

Editable text- Effect>Blur>Gaussian blur- then play with the setting-