Its not a local code issue, its an issue with the service panel itself. Read the sticker, somewhere it will specify the max branch circuit allowed on the buss. The panels that allow this special 4p breaker will have language that specifies the part number for it.
If you use a 150A 4p to feed your backup system, and a 50A left on the distribution bus, you are only giving up the flexibility that all the loads in the backup system need to work out with the load calculations of the 150A breaker. Its a pretty small difference imo. In other words if you try to add another large load to the backup system, the load calculations need to work out with 150A. Difference is on the orderof 20-30 amps of "calculated load" you leave on the table.
When your company runs the load calculations, if they come out with for example 147A (I'd call this marginal for a 150A breaker), this basically tells you you can't safely add additional loads to the electrical system. In that example, if you had you run the calculation with the car charger on the backup system, and the main breaker at 200A, its likely the calculations result would be 175A-ish so you could theoretically add a small 25A load. Its a pretty small loss.
If they come up with 173A, then this plan will not work as a 150A breaker is undersized.
Also the 100% rule states that the addition of all breakers nameplate rating must not exceed the bus rating. So if you leave a 50A on the bus for your 14-50, then its a 150A max breaker for the backup system.