You cannot simply keep typing. Word continues formatting.
What you are seeing as black is probably "Automatic" which is a good thing.
When you want to start typing in the underlying color for the paragraph style (Automatic), press Ctrl+Spacebar to remove direct formatting.

I would advise you to create a character style for your blue text rather than simply applying the color. You can attach a keyboard shortcut to your style if you want. This way, if you want to in the future change all of your blue text to red, you can just change the style definition to red.

• Importance of Styles in Word
• Assigning Keyboard Shortcuts in Microsoft Word 2007-2021 (365)
• For keyboard shortcuts instructions, take a look at Assign Keyboard Shortcuts by Suzanne Barnhill, MVP. It has more for the menu versions of Word.