Not quite how that worked out.

Yes, the Ottoman empire did either outright cut off the spice trade to mainland Europe or heavily tax it, which caused Portugal and Spain to seek sea routes to the Far East.

The Portuguese claimed the route around Africa as theirs. It was long, but not too long. The route was known, and you don’t have to sail far from the coast the entire way.

To say Columbus was “commissioned” was a bit much. Columbus went to great lengths to approach the Spanish crown to propose his “going to the East by sailing West” plan, which was based on some bad math. Like he read an Arab scholar’s work on the subject which gave the Earth’s circumference in Arabic miles, which he read as the shorter European miles, so he underestimated the size of the earth by about 1/3. The cartoon I was shown in elementary school depicted Columbus as the visionary who first thought the Earth was round, when it’s quite the opposite. It’s more like he was a crackpot small earther. But he did finally convince Isabella and Ferdinand to sponsor a voyage. Three ships departed Lisbon in 1492, sailed down the African coast to the Canaries and then did something monumentally stupid: They made a right turn and headed due West straight out to sea.

Columbus, if not his men, deserved to sail out to sea and starve to death eight time zones East of Japan, but in the most impactful stroke of dumb luck in human history right about where he predicted Southeast Asia and the Spice Islands to be, he found Central America and the Caribbean. Columbus ended up making 3 more trips to the Caribbean, he saw the shores of Mexico, the mouth of the Orinoco river, was shipwrecked on Jamaica. He went to his death believing he had visited Asia and did not believe he had discovered a New World. Credit for realizing “Look, we’ve sailed 400 miles down the coast, there’s no way this is Indonesia” goes to Amerigo Vespucci, and Ferdinand Magellan actually achieved reaching the Spice islands by sailing west from Europe, though most of his men including Magellan himself died in the process and what few men remained completed a circumnavigation because starving on the way back across the Pacific sounded less fun than possibly dealing with the Portuguese.