No-Coverage Answer
The Taygetan contact material does not describe the farthest point of Taygetan exploration or discuss whether they have approached the boundaries of the universe. All operational descriptions in the corpus concern activity within the Milky Way — travel between star systems, Federation meetings, Earth orbit operations, and journeys to specific planets within our galaxy.
The material does discuss faster-than-light travel mechanics in extensive detail (stellar navigation series: 023, 057, 243, 280, 282), solar portals/wormholes connecting distant points within the galaxy (132), and the theoretical framework that allows interstellar travel. But the question of how far they have actually gone — or whether the universe has reachable boundaries — is not addressed.
See also: At what point in Taygetan development did they acquire interstellar travel? (covers the mechanics and history of Taygetan space travel)
Searched: All 834+ transcripts, enhanced topic index. Grep for "farthest," "furthest," "boundary of universe," "edge of galaxy." No relevant results.