How to automatically type ordinal numerals superscript (1st, 2nd, 3rd etc)?

In the Emoji & Symbols panel, just enter individually the letters you want as superscript ordinal numeral suffixes. In the font variations sidebar, you will find a superscript version of that letter. They are present for d, h, n, r, s, and t. They won't be identified as superscript per se but will bear the name modifier letter small h. For instance, the letter h:

Now, you have the building blocks to create. your replacement string 3ʳᵈ, etc. This still won't match MS Word's visual results though.

This may not be possible. Common fractions like ½ and ¾ are actual characters in the font. In contrast, generally speaking, superscript is a style in which characters can be displayed.

Only some apps, like Pages, have the ability to apply superscript style. I can't use superscript in this reply to you, for example.

On the other hand, Unicode now specifies a great many subscript and superscript symbols. In fonts that support them, these are characters in their own right, like the fractions. But they're not designed for representing English ordinals, and are often inconsistently sized: 1ˢᵗ and 2ⁿᵈ for example.

Some months ago, I was thinking about the matter of superscript ordinals in general, and decided to research it a bit. It turns out that many style guides specifically recommend against writing English ordinals in superscript. If you look at professional printed publications, you'll see. And this, I reckon, is why Apple has chosen not to enable automatic superscripting of ordinals in Pages by default (it's available in Preferences).