I get paid for code that works, not for tests, so my philosophy is to test as little as possible to reach a given level of confidence -- Kent Beck (author of the first TDD book).
If I go for a test-by-test approach, and just add the first test, I cannot just add a reusable code in the implementation, cause it does more than the test currently asserts about
Key idea: we do the TDD ritual when we want the results that the ritual will produce, not just for the sake of doing the ritual. Nobody is running around awarding prizes for how deftly you navigate the red-green-refactor loop.
Write your one test, make it pass, clean it up, move on.
You should write the tests that help get programs working and keep programs working. Nothing more. -- Beck (Extreme Programming Explained).
Now, you are making a trade-off, in so far as the collection of tests that you have for this new component is not as comprehensive as it might have been had you built this part of the program first (before you had your wheel).
Which is to say that, although the design is satisfactory, you haven't captured all of the constraints on behavior in code.
So there's possibly some risk that at some point in the future, the requirements for the well tested thing will diverge from the not-so-well-tested thing, and someone meaning well will put the change in the common code, run the tests, and "everything works" because the testing isn't adequate to detect the regression in not-so-well-tested thing.
It's not really a TDD tradeoff, as such, because the design is "fine" up until the point that you discover that the old and new behaviors should diverge. But if you are in a culture that expects that the tests will be best-effort-complete, then you may need to pause the TDD work and fill in the missing automated tests.
The good news is that because you've laid the groundwork already, you "know" that you are going to be able to write cost effective "unit" tests, because you've already shown that the test subjects can be effectively isolated and fed controlled data.
(Recommended reading: chapter 4 of Accelerate by Nicole Forsgren)