The base resolution for Shantae is the standard 1920x1080. That is the resolution at which the high resolution story characters and interface elements are prepared at as well. The text is probably rendered in the engine as regular text. I don't think it is using a bitmap based character set, but rather the regular font file (ttf, otf) to render the text.
The pixel art graphics are scaled up 6 times within 1920x1080 and originally prepared for a screen at 320px by 180px. There is a black margin used in the game as well, though, so the actual viewport resolution is less than those values it seems. Still, you could just replicate those resolutions for your pixel art and HD assets.
But I have no clue about the development environment that was used for this game, so the font tech used here involves some guesswork.
Which means that if you want to replicate this same effect, you would prepare your high resolution gui assets for 1920x1080, and your pixel art for a screen size of 320px by 180px (1920x1080 divided by 6).
Implement the text as you would normally do in GM. Add a new font sized around 32-36, and use it to draw your text in the game.
Here is the screenshot downscaled 6 times. Notice how the pixel art does not change.
PS you could have figured this out by yourself by opening the screenshot in any image editor.