That is an old "rule of six" panel, which while grandfathered, is illegal under its grandfathering becuse it has 7 main breakers. Going to five is a good plan.
It is a classic "CH" panel which is a very good industrial grade panel, except that the 3/4" breaker width make non-ordinary breakers very expensive (a trait it shares with Square D QO). That makes it perfect for what you plan.
On your subpanel which would be near this panel, I would get a panel with a main breaker, with an eye toward (at some point in the future) cutting it over to be the main panel. In a subpanel, the "main breaker" is nothing more than an on/off switch, it is OK for it to be larger than the feeding breaker.
I would also get a rather large panel, at the very least 42 space and even 60 or 84 if practicable: because panel spaces are dirt cheap and often even come with free breakers, whereas running out of space is painfully expensive.
I would aim for an industrial grade panel of good repute (one available in 3-phase variants, not Homeline, BR, or second tier brands) and avoid the expensive 3/4" breakers (not CH or QO).
Over time, as you find it convenient, i'd migrate all your 1-pole and smaller 2-pole circuits over to the new panel.
For your garage panel anything would do, but I'd go for the same type as your indoor panel, so you can use some of those bonus breakers. Again it's false economy to scrimp on spaces, I'd go 20-30 at least.
Also, since garage spaces need to be on GFCI, consider getting a subpanel which has a "main breaker" which is GFCI, that way all the breakers in that panel would be protected (at the cost of potential nuisance trips, a big deal if you keep a freezer in the garage).
Ed Beal raises some very good concerns about overall capacity. One problem with these "rule of six" panels is there is literally no main breaker to stop you from drawing more than 150A. So it pays to be conservative.
It's a difficult situation because you have two big loads that operate sporadically - the EV charger and the range. And the A/C as a wildcard.
One thing I might suggest, is feed the garage subpanel from the new primary subpanel. And then move everything but the range over to the new subpanel. At that point the only things still in the CH panel would be a 60A range breaker and a 100A subpanel breaker. Even at max, those two could not overload the 150A service (by enough to matter). This would force your entire house (from A/C to EV charger) to share 100A, but would remove the possibility of an overload. This would also save you the $85 you'll spend on a second 100A CH breaker.
Was the bozo that wired those circuits trying to burn your house down?
Assuming that the wires are 10AWG (i.e. 30A), this is a major problem indeed as the wires can overheat badly from excessive current draw before the breaker ever notices something is wrong! Think of what a live toaster element inserted into your wall would do...
As to the Code, your issue violates 210.19(A)(1):
(1) General. Branch-circuit conductors shall have an ampacity not less than the maximum load to be served. Conductors shall be sized to carry not less than the larger of
210.19(A)(1)(a) or (b).
(a) Where a branch circuit supplies continuous loads
or any combination of continuous and noncontinuous loads,
the minimum branch-circuit conductor size shall have an
allowable ampacity not less than the noncontinuous load
plus 125 percent of the continuous load.
(b) The minimum branch-circuit conductor size shall
have an allowable ampacity not less than the maximum
load to be served after the application of any adjustment or
correction factors.
and 240.4 (the exceptions in A-G do not apply to your case):
240.4 Protection of Conductors. Conductors, other than
flexible cords, flexible cables, and fixture wires, shall be
protected against overcurrent in accordance with their ampacities specified in 310.15, unless otherwise permitted or
required in 240.4(A) through (G).
Best Answer
Let's start with the easy answer. If your installation manual is calling for a 40A circuit for your cooktop and you should install it per their directions. This is because the manufacturers engineers have determined that the recommended circuit is necessary for the cooktop to operate properly. Failure to do so could void the manufacturer's warranty if there is a problem with the cooktop.
Now the more confusing part. NEC Article 220.55 covers calculations for residential cooking appliances and it does allow derating of these circuits. For example if you have a range rated at 12K you can install a circuit rated for 8k. You can run a single circuit for more than one cooking appliance and tap the circuit for the reduced load of each appliance. I have to say that it is one of the most confusing and complex calculations mentioned in the NEC.
How can you be sure that what you have will work with your new cooktop?
You are on the right track by reading your manual and trying to determine the correct KVA to your cooktop, but what you really need to find is the Nameplate rating of this unit. It usually is not in your Installation Manual and it may be hard to find on the unit itself but it will be there somewhere. Another place to find it is to go online to the manufacturer and see if there is a specification sheet for the unit. On the nameplate you will find it's operating voltage and amperage or the required KVA. Then you will have to take that rating and calculate the demand from NEC 220.55. Personally I think that it needs to be supervised by a professional Master Electrician or Engineer or a very competent Journeyman.
Hope this helps, good luck and stay safe.