Analogy: If you need to pay a bill (in ye olden days of paper checks), you need to have a blank check in your checkbook and you need to have money in your account.
There are two different issues that come into play when adding a new big circuit such as an EV charger.
This is the problem you already know about. There might be a relatively inexpensive solution, but we need more information to figure that out. Specifically, many panels have half-size/double-stuff/tandem breakers available. These put two ordinary breakers (typically 15A or 20A each) in the space of one. However:
- The panel must allow for them generally
- The panel must allow for them in the places you want to put them (some say only top, only bottom, etc.; some have a maximum limit)
- They are not available with AFCI or GFCI
In your case, that means the only spaces possible for doubling up are 1, 3 and 5. All the others have TEST buttons, which indicates AFCI and/or GFCI and not available in half-size breakers. However, if you replaced 3 and 5 with a half-size pair in 5 and move 1 to 23, you would have 1 and 3 available for a 240V double breaker.
The utility only provides a certain amount of power - e.g., 200A service. Each panel will have limitations as well. You can have breakers that add up to far more than your total service (you currently have 240A on one leg and 220A on the other, very likely more than the feed to this panel) because most breakers, most of the time, use far less than their rated capacity. In fact, the circuits that run for long periods of time (e.g., water heater, air conditioner, EV charger) are derated - e.g., a continuously running appliance that actually uses 40A will be on a 50A breaker.
The way to figure out what your utility service and your panel can truly handle is a load calculation. This takes into account various things, including the various typical large loads (water heater, dryer, oven, etc.), typical usage in kitchens and bathrooms, an amount per square foot to cover general usage (receptacles and lighting) and any specific extra loads such as EV charging.
In general, adding any big load should trigger a load calculation. In reality, most of the time things get added incrementally and it doesn't happen. But with a nearly full panel and a potentially huge extra load, a load calculation is essential before proceeding.
If the load calculation indicates that your service will be overloaded by adding the EV charger, you need to talk to your utility to find out about what options are available to increase your service.