I looked through the documentation as best as I could, and I did not find a maximum points for optimization, just that 500 point limit per day and 40 per minute.
Is there a way to route cycling directions through 150 points. They are all within the same city, so it should be a route about 250 miles long.
This is possible with ORS but not on the public instance. Optimization is a very compute-intensive task, therefore, the optimization endpoint is limited to 50 routes.
See API Restrictions | Openrouteservice for further details.