How do I resize the scale of the upgraded graphics text flexibly?

Try this.
https://srt2xml.com/
convert your .srt into .xml then drop it into PR
Open it as a sequence then you can get the graphics and the transform way you want.

I assume you are trying to change the font size without dragging the bounding box.

No, you can't get rid of the box, and I don't think you can change the font size with the mouse in the Program Monitor.

You can use a keyboard shortcut, such as "Increase Font Size by 5 units" - Ctl+Alt+Shft+Right arrow. This does not change the bounding box, but if you don't change the bounding box, you get other problems.

There are two types of text boxes. Point text is created by clicking with the Text tool and typing. The bounding box expands as you type, but does not word wrap. So the box (and text) will run off the screen to the right if you type enough. The Text/Transform “position” is the bottom left of the TEXT, not the bounding box. And the Anchor Point is the same (a zero, zero adjustment from position).

Paragraph text is created by clicking and dragging the bounding box before typing text. This word wraps as you type, but the box does not change. If you type until the text fills the last row of the box, the text scrolls out of the box and out of view. The Text/Transform “position” and Anchor Point is the left/top position of the bounding box.

Caption text is “paragraph” text, and inherits that characteristic when using Upgrade Caption to Graphic.

How you address this depends on what you are trying to do.

Stan