Which tools can identify scholarly papers that use the same types of equations?

There is MathWebSearch; from the site:

The MathWebSearch system (MWS) is a content-based search engine for mathematical formulae. It indexes ​MathML formulae, using a technique derived from automated theorem proving: Substitution Tree Indexing.

Indeed, zbMATH, already uses it to provide MathSearch. The interface uses LaTeX syntax. (MWS itself seems to support different interfaces.)

Approach0 is able to find expressions with different variables:

https://approach0.xyz/search/?q=%24%5Cnabla%5Cleft(k(T)%5Cnabla%20T%5Cright)%24&p=1

However, its index does not include academic papers, it is only indexing Math StackExchange now.

That being said, I think this is still an option since Approach0 is open-source, and you can use it freely to index whatever content you want to perform search on. And in the near future, approach0.xyz is very likely to further include academic PDFs into its index. Just keep an eye on it!

I know this is already answered, but searchOnMath looks interesting too. Maybe it suits your needs.