Just bought an electric car. Do I need a bigger panel?
If you have space alongside this panel (at least a full stud bay's worth to one side)...

If you have a full stud bay's worth of space to the left or right of this panel to mount another breaker panel, then mounting a second panel and using it as a subpanel is your best bet here.  A 24-space, 125A, main lug  Homeline subpanel (HOM2448L125PGC) is inexpensive, provides sufficient expansion space, and comes with a ground bar already fitted -- with this, a trio of 1AWG Al wires in a 2" rigid metal conduit nipple would connect a HOM2100 breaker + a LK125AN neutral lug on the neutral bar in the main panel to the main lugs in the subpanel, providing a 100A feed to the subpanel.

In this setup, the HOM2100 replaces one of the A/C breakers, and both A/C breakers move to the subpanel, with 10AWG pigtails through the conduit nipple connecting the hot wires from the A/C breakers to the existing wires out to the air conditioners.  The circuit to the car charger can then be run off a HOM220 breaker in the subpanel, and blank-out plates (HOMFP) installed in the empty spaces in the main panel.  The branch circuit neutrals would land on the neutral bar(s), while ground wires would land on the ground bar(s), and the green bonding screw would not be installed into the subpanel (or removed if it was installed at the factory).

If you don't have room for a subpanel

If there is no space available for a subpanel, an alternative option would be to use a HOMT220230 quadruplex breaker instead of one of the A/C breakers -- the A/C circuit would land on the two 30A poles, while the car charger circuit would then land on the two 20A poles.  This is less expensive than a subpanel, but does not provide any expansion room, unlike the subpanel option -- I'd favor the subpanel in your case considering how full your main panel is.