Are there published testimonies from Christians who independently discovered the doctrine of the Trinity on their own by just reading the Bible?

The simple answer is: there are a lot, in the form of Trinitarian theology books published by professional theologians. One example is the 2021 book Contemplating God with the Great Tradition: Recovering Trinitarian Classical Theism by a professional theologian and Baptist minister Craig A. Carter reviewed here and discussed in an interview here. For an example of the continuing relevance of the Nicene formula for today to battle new understanding of God that is NOT Biblical, read his July 2021 Credo Magazine article Why We Must Reject Social Trinitarianism: It is neither Nicene nor Biblical.

• Surely a professional theologian who, by virtue of their training is well versed in exegesis and philosophical/historical/theological nuances of the critical terms used, is qualified to submit a "testimony" despite that the reasoning used comes from objective sources and methods?
• Surely if the objective source & method is enough we do not need special subjective revelation/prophecy/insight, which would then dilute the applicability of this Divine Truth to those do not possess similar subjective revelation?
• Surely we would not want to label the objective reasoning as "private interpretation" since many other theologians over hundreds of years being raised in multiple cultures and mother-tongues came out with the same conclusion?
• Surely we don't expect a non-professional theologian to come up with word-for-word definition of the Trinity as though it comes by dictation of the Holy Spirit, since the original 4th-5th century formulation itself came after many deliberation by church fathers who themselves were professional theologians?

Granting that the Bible alone may give support to non-Trinitarian positions, and that some pruning of theological options by the early church fathers is necessary to come up with the orthodox formulations of the Trinity, it is invalid to infer that these pruning is necessarily due to special insight / revelation to special church fathers (subjective) because then it could amount to the necessity of an oral tradition or of the necessity of prophecy beyond the canon. Instead, the standard mainstream narrative is that the Apostolic Tradition preserves the deposit of faith from the original apostles (1 Tim 6:20, 2 Tim 1:14, 1 Cor 11:2, Col 2:8) and this pruning / preference is simply due to a growing explicitness of a position held by the apostles from the very beginning. The ultimate test would be: if there is a time machine and that the apostles were present in the councils of Nicaea and Chalcedon, they would side with the orthodox theologians.

Thus, according to standard mainstream narrative, the creedal formulation of the Trinity is fully Biblical since the seeds are there. We can then logically and reasonably hold to sola scriptura's principle of the sufficiency of Scripture (see an argument for this in a 1997 Christian Research Journal article What Really Happened at Nicea? by evangelical Reformed apologist James R. White). Later prophecy / revelation a la LDS's Book of Mormon is not needed

CONCLUSION: What matters is that the formulation is consistent with the whole Bible.

• It does not have to be the only interpretation possible, but should NOT have to rely on unnatural / strained interpretation of certain Bible verses.
• It can use Greek philosophical concepts as long as they don't corrupt the original Hebraic conception of God implicit in the OT. After all, the Greek Septuagint used by the apostles necessarily used Greek words to translate the OT, which in some instances expanded the original meaning of the words outside the Bible. Similarly, just because the formulation of the Trinity is using terms not found in the Bible and the terms were put in service BEYOND the Latin/Greek non-Christian usage (see Substance and Person in Tertullian and Augustine) it doesn't make it unbiblical.
• Expecting non professional theologians to come up with word-for-word definition of the Trinity is as unrealistic as expecting an engineer to re-discover Newton's / Einstein's law of physics. What matters is that the Physics formulas are consistent with how things act in nature and that the Trinitarian formula is consistent with what God has revealed of His nature in Jesus and in the Bible (as a record of the sanctioned prophets and original apostles's deposit of faith).