How can I add breakers for a new HVAC system to a full panel?

The first thing to consider here is whether the utilization of either service leaves some of the service's capacity available for other loads.

The capacity of the service depends on the service conductors and equipment - the size and makeup of the wires going to the utility, the service equipment panel's rating, and the main breaker size.

The number of unused slots in the panel doesn't determine utilization. It's possible to have lots of open slots, but all the available capacity used by the breakers already present. If that's the case you can't add additional circuits, you'll trip the main.

It's also possible to have all the slots full but not utilizing the available capacity. If that's the case you can add a subpanel to make room for the additional circuit without tripping the main.

You can only upsize the hot water heater service breaker if the service conductors and equipment (panel, disconnect, etc.) can handle the additional ampacity.

You can determine the utilization by having an engineer or electrician do a load calculation, which approximates the utilization based on the square footage, appliances, etc., or by monitoring the actual utilization for a period of time to determine the peak utilization with your present configuration.

That utilization info will tell you whether each service would need to be upgraded to handle the additional load, and you can determine which service makes more sense for the mini-split.

Option 2 is probably not an option at all - that setup is almost always for a special-rate storage electric water heating tariff and is only on for a few hours when demand is low overnight (which is why it's a special lower rate) or else it's switched off whenever loads are high (a different scheme, similar concept.)

For my utility, you can keep them if you have them from decades ago (when they had a nuke plant idling away all night), but you can't get a new one done this way. You certainly cannot add to it, (for my utility) you don't own the water-heater associated with it - it's part of the overall deal, they own it.