On Bibliography of Quaternions and Allied Mathematics by Alexander Macfarlane I found this:

On page 72; James Byrnie Shaw
1896 Sedenions (title). American Assoc. Proc., 45, 26.

I couldn't find this reference, but the same author wrote this book:
Synopsis of Linear Associative Algebra: A Report on its Natural Development and Results Reached up to the Present Time. 1907.
From its Table of Contents; Part II: Particular Algebras. Section XVIII: Triquaternions and Quadriquaternions. Page 91.

Early on Sedenions were also known as "quadriquaternions".

Section XIX: Sylvester Algebras. Page 93.
Covers "Nonions" (9-ions), and "Sedenions" (16-ions).
Here the Sedenions are attributed to James Joseph Sylvester.

On page 76; James Joseph Sylvester
1883-4 On quaternions, nonions, sedenions, etc. Johns Hopkins
Univ. Circ., 3. Nos. 7 and 9. 4, No. 28.

This second reference can be found among The Collected Mathematical Papers of James Joseph Sylvester, [Volume IV(1882—1897)]:

Sylvester, James Joseph (1973) [1904], Baker, Henry Frederick (ed.), The collected mathematical papers of James Joseph Sylvester, IV, New York: AMS Chelsea Publishing, ISBN 978-0-8218-4238-6

Then, as far as I understood, James Joseph Sylvester appears on the literature as the proponent of two Algebras; the one from the Nonions and the Sedenions. I will leave as an open question for the community to confirm, correct, or debunk that J.J. Sylvester "discovered" or "was the pioneer" of their study in 1883.