It's nearly impossible for anybody to tell you if you can safely add a second subpanel, based on the information you've provided. It's going to depend on the service capacity, and how loaded the service already is.
Your best bet would be to contact a local licensed Electrician, and have them do an estimate on adding the new subpanel. They will come take a look, and should tell you what would be involved in adding the panel. This will give you a better understanding of what your options are, and an idea of how much it would cost to simply have a professional handle the job.
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
Never, ever scrimp on a panel
When I hear "100A panel" I tend to think very small panel. Don't get caught by that. Spaces are cheap, and you want loads of extra spaces. Firstfor future expansion (it's frustrating not to be able to add a feature for lack of spaces). And second, when the inspector comes 'round and says "these circuits need AFCI". My goal is to finish a project with less than 50% of spaces used (but without using double-stuff breakers). A neat thing about panel pricing is you can get industrial tier panels like CH, QO, GE or Siemens for about the same price as tenant tier lines like Homeline or BR.
Wire size
In aluminum wire, you need
There is a "100A bump" because circuits >=100A get to pull out of the 75C column in NEC Table 310.15B16 instead of the 60A column. However in your case the numbers don't quite line up; 2AWG is rated 75A@60C and 90A@75C. You can "round up" to the next breaker size, so 60C gives you 80A breaker. Sadly, 90A breakers do exist, so you can't call it a 100A circuit (unless your AHJ agrees; worth asking since this is quite close and there's precedent).
100' is below the 115' threshold where anyone even starts to care about voltage drop. If you want to upgrade wire sizes to deal with voltage drop, that is fine, but feel free to upgrade breaker sizes also.
I don't know what your total project cost is going to be. Obviously if this all DIY the wire cost is a significant fraction, but this ignores the value of your time. Contracted it's at least a $600-1000 job. A small increment in wire costs can give you a lot of headroom in the future. It'll even help with home resale value.