If you have hit vehicle limit, there are some things you can do to possibly save your city.
*Bicycles count as vehicles, get your citizens to use Mass Transit.
*Reduce the amount of vehicles your Mass Transit uses. Example, a Super Bendy Bus is 3 30 seat buses. If you have 10 on one line, then it is actually 30 vehicles. I use a lot of 60 seat double deck buses( Airport DLC and Vehicles of the World CCP) and the 70 seat bus from the Railway of Japan CCP. You should look at all types of Mass Transit to see if you can reduce how many your using, there are several sizes of Trams.
*Set up a Cargo Train network to move cargo over distances. Be mindful they are wonky to work with. With practice they can be very effective.
*Reduce some services around your city, I reduce Post Service to 50% to reduce how many trucks are spawned. Do you really need Taxis, one vehicle moving one cim, but cooler than a pocket car.
*But probably the most helpful thing you can do is optimize your traffic flow %. Any place you have heavy traffic flow, see if you can improve the flow. Improve your Highway connections. Give them more options to get where they want to go. Proper Lane Hierarchy and Biffa style lane math helps a lot. If your not familiar with this idea, watch Biffas YouTube fix your city series. He explains it well.
*Every city is different, I have one that has hit limit 3 times before, but I'm struggling to get it under control again. It may be time to dezone some areas to reduce traffic to save it.
* I have had more problems in some maps. I believe it's the outside connections not being able to spawn/despawn fast enough. In cinematic camera view at night, I could see a traffic mess in the fog. Or maybe I build to fast. So maybe go slower when necessary.
I hope this helps.