Repeat last modification to text

Nope, never worked this way. Your formatting is sticky - meaning whatever you set in the character / paragraph panels will stay that way until you change it again. If you have a type layer selected and make changes to the character panel it will change the existing type. 

"when I changed formatting of a word or a letter and immediately after I selected another word or letter, the same modification was applied, without any further command"

Not in Photoshop, that feature was never present in Photoshop.

Hi @Luca5FC3 

The only way that would happen would be if you were properly using Paragraph Styles for the entire paragraph or Character Styles for the words that had different formatting from the rest of the paragraph. If you edit the style, all text using the style will update.

https://helpx.adobe.com/photoshop/using/formatting-paragraphs.html

~ Jane