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.
Best Answer
There are a whole bunch of issues here, but let's boil it down to 3 of them:
Load Calculation
The proper way to figure out how much power is allocated, and therefore how much is available, is a Load Calculation. This is a relatively complex way of adding up:
etc.
You don't do a load calculation by adding up breaker panels - that would normally be way more than it needs to be.
You don't do it by putting a clamp meter on your feeder - that is not a reliable way of calculating the load, unless you do that all year long to find out the peaks (which you can often get from your utility web site).
An example, which to me looks good, of a load calculation web page worksheet is here. You are supposed to do a load calculation any time you have a major change in your service/usage - my electrician did one as part of my heavy-up even though it was abundantly clear there wouldn't be an issue (heavy-up for panel replacement and generator, not to add new circuits).
In order to figure out how much capacity you have available, you need to do:
So that tells you how much capacity is available. If it is 50A, great. If is only 20A or 30A, you are also OK for EV charging - more below.
Rule of Six
You have a Rule of Six panel. That means you have up to 6 double breakers (or other "pulls" - I had fuses to be pulled out + breakers) to turn everything off. Generally obsolete, but if working OK with a still-available, not dangerous, panel then perfectly fine. One of those 6 breakers controls the bottom of the panel. In your case, as is typical, that is a 60A breaker - 60A being the largest inexpensive breaker for many panels for a long time. (Expensive large breakers is one of the rationales for Rule of Six panels - no need for a 100A or larger main breaker.)
So if you add anything to the "lighting section" you would need to do a load calculation first, but you already have that full with half-size breakers, so nothing going on there.
The other top 5 breakers are 3 x 30A, 1 x 50A and 1 x 100A. According to a comment, the subpanel is connected to the 100A breaker. That should be fine for the existing loads because of the way load calculations handle multiple cooking appliances (2 x 40A in your subpanel) but you may be pushing towards the edge of your capacity on the subpanel. You can probably add 20A or 30A to the subpanel, but almost certainly not 50A.
You really need to find out what your utility service is before doing anything else. If it is 100A, which was quite common in Rule of Six days, then you may already be in trouble.
EV Charging
This is the driving force here, which is quite understandable. The typical sizes thrown around for EV charging are 50A and 60A. Why? 50A is a standard that comes from the RV world, which has resulted in 50A being a common travel charger size. 60A is the maximum possible capacity on many home EV chargers (EVSE is the official term). But the reality is that most people (a) don't need that much capacity and (b) don't have that much capacity available. You almost certainly don't have the capacity - I would be surprised if you could squeeze out much more than 20A of capacity after doing proper load calculations. But you also most likely don't need that much capacity. A 20A circuit charges at 16A (80%) - that's just under 4 kW. 4 kW is roughly enough to add 12 miles of charge to an EV (varies by model). If you charge for 8 - 10 hours while you sleep, that will add 100+ miles per day. The average US miles per year is 13,500 but varies by state. That's less than 40 miles per day! 100 miles per day of charge is more than enough for most people for a typical commute, errands our town, etc.
So the bad news is you are likely due for a heavy-up. If you have 100A service then I really think that makes sense. If you have 200A service then you probably have enough capacity to add EV charging to the mix, but you will likely need a new panel or some very careful reconfiguration of the existing panels to make it work.
But the good news is that you don't need to work in 50A, just 20A, or 30A if you want to splurge, will be plenty.