You need to do a Load Calculation. Actually, two of them - one for the utility service/main panel and another for the subpanel. You are adding 50A to your load. That's 1/4 of a typical 200A service, so it is significant. It is even possible to have smaller service if your cooktop, water heater and heating are all gas.
Update: OP uploaded pictures of two 200A main panels, and both have plenty of space in them. That hints at a possible 400A/Class 320 service. If that's the case then total load will almost certainly be fine for the new cooktop and at first glance the subpanel feed of 90A is likely to be fine as well. But actual load calculations are needed. Except technically three load calculations:
- Total service
- 200A panel that feeds the subpanel
- 90A subpanel
But assuming this is a normal 400A -> 2 x 200A, the total service really shouldn't be an issue.
Your gas cooktop may had a dedicated 20A 120V circuit, but the actual usage would have been < 1A and only for a few seconds at a time, as opposed to 40A 240V for a long time and peaking at 48A 240V.
There are online calculators available. Note that a proper load calculation is not "add up all the breakers" and is not "stick a clamp meter on the main feeder and see what it shows" (though that can be useful in certain circumstances).
Basically a Load Calculation takes into account:
- Size of your house
- Required dedicated circuits (kitchen, bathroom, laundry)
- HVAC (largest of H or C)
- Large fixed appliances - e.g., water heater, pumps
- Cooking appliances - these get some special rules, but replacing a gas cooktop with an induction cooktop will definitely increase the load
and a bunch of other things.
If your subpanel has room then it is just a question of breaker spaces (which you have), the right size of wires, etc. So do the Load Calculations - to make sure you have enough capacity in your service and enough capacity in your subpanel (subpanel total capacity is determined by the breaker feeding it in the main panel) and if there is enough to add 50A, great. If there is not enough then we can discuss possible solutions.