Umm, 2Tim. 2:15 is nevertheless the very definition as of today even as of Robert Cawdrey in 1604 or before that. Your definition of its older users is quite incorrect when applied to 2 Tim 2:15 based on the context. Still desirous of learning is meant when we study, it’s all about learning! The 1604 A Table Alphabetical by Robert Cawdrey does not give the full definition of what study means and yet only a derivation. We have so many dictionaries before that that does tell us also of learning things, the accusation of knowledge, application of the mind, to record in the mind, muze, thought, a library, a great number of books, etc. So, in translation, we have to remember context plays a very important role. I have no problem with 1 thes. 4 and it could mean diligence but not on 2 Tim 2:15 and the KJB is right and not in error.
Here’s the definition in 1611 by John Florio in regards to study
John Florio, Queen Anna's New World of Words (1611) (partial)
Stúdio,an earnest bending of the minde to a thing, affection to doe good or euill, study, endeuour, diligence, industry, laborious desire, mentall exercise.
Stúdio,a priuate study, cabinet, closet or any place to study in. Also an vniuersity where studies are profest. Also a Colledge where Students are. Also a standing deske in a schoole for great bookes.
Bibliotheca Scholastica
John Rider (1589)
To be Pensiue, or sorowfull.
... or careful. 1 Æger, mæstus, ad. vide careful. Pensiue, or as it were in a brown study 1 Meditabundus, cogitabundus, cogitativus, ad. Somewhat pensiue. 1 tristiculus Pensiuely, sorowfully, ...
import_contacts To Studie, or applie the minde.
... 1 Opera, f. vt operam dare alicui scientiæ, To emploie their whole studie, &c. A study by candle light. 2 Lucubratio, f. A releasing from studie. 1 Avocamentum, n. Studie, or loue of wisedome. ...
To be Wise.
... or prudence. 1 Prudentia, sapientia, sophia phronesis, 2 sagacitas, solertia f. sal, m. Loue, or study of wisdome. 1 Philosophia, f. wise, or prudent. 1 Sapiens, iorissimus, prudens, consyderatus, consultus, .