First start off with a load calculation for existing structure.

Then a load calculation for addition.

Then check size and BTU output of existing oil burner. To e clear this s a boiler or forced air furnace.

For good comfort, I think it would be a big mistake not to add addition to existing system or perhaps even consider a separate system for addition.
You are fooling yourself if you believe orientation of new addition and residual heat from existing structure will be satisfactory. Not clear what is covered by the $1400 charge but this seems like a very inexpensive solution assuming you have capacity from existing system.

I would not take any shortcut on insulation for the new addition.And be aware that heating and cooling a large area with cathedral ceilings has to be carefully designed and sized.

This is one time I wholeheartedly agree with your GC.

BTW, what is your location?

IMO

How much insulation will be above the cathedral ceiling? Will it be a flat roof?

The room has a lot of west facing glass. It is going to get much hotter in the summer than the rest of the house. In the winter a lot of the warm air is going to be up at the ceiling. If you want this room to be as the same temperature as the rest of the house then you need a minimum a separate zone.

Thank you for the feedback. We are in New England, so we are definitely concerned about keeping the room warm in the winter. To be clear- the room will have it's own heat (a baseboard system) so we're not just relying on the airflow from the rest of the house. We have an oil burner and can't remember what the capacity is, but everyone who's looked at it has said that the capacity is fine. I guess I just don't understand why it will be any colder than the rest of the house without the zone. It's an older house with virtually no insulation in the walls and the new part will be well insulated with new windows so it seems like it should be warmer. We're adding a ceiling fan to help mitigate the heat loss from the high ceiling. We don't have central air so we'll just have a window unit for cooling. Also I am skeptical because I feel like if it was obvious that we needed another zone, then our contractor should have built it into his initial quote.

I assumed you had central air conditioning. If you are going to have a window unit in the kitchen, then that effectively is a separate zone. You should be fine in the summer assuming the window unit can keep up with the heat gain of the kitchen. One window unit in such a large space may not be able to keep the temperature even throughout the whole kitchen when the sun is beating down on the windows. Think about two smaller units installed at opposite ends of the room.

It is difficult to say if kitchen will have the same temperature as the rest of the house during the winter. It is better insulated, but it has a lot of windows and a high ceiling. It will be probably fine during the day, but may be cold during the night.

How many feet of baseboard will be installed? To what temperature do you set the thermostat during the day and night?

If you don't want to spend the money now, then I suggest install the new plumbing for the baseboard so that it will be easy to zone in the future in case you are not happy with the temperature of the kitchen. I would also run the wires for the thermostat now in order to make it easier in the future. Thermostat wiring is inexpensive and simple to install when the studs are exposed.

Perhaps I misunderstood from your OP.

You have an oil fueled boiler for hot water baseboard heating system.

You have capacity to add baseboard hot water system to addition.

The $1400 is just for making the addition a separate zone with it's own thermostat that can be cut on/off independently from original system and structure.

I see no reason for doing this either other than it might save you some fuel oil.

I assume we are talking about heating only and air conditioning is not part of this HVAC addition project.

Post back.

IMO

Thank you both the feedback- I think we are going to do just as mike_home suggested and ask them to do their best to make it easy to add a zone later if we want to. I'm not sure how many feet of baseboard we're getting. We keep the thermostat at 62-64 during the day and 58 at night. I've been asking friends what they have and seems like more folks have issues with multi-zone systems so I think it makes sense to try to live with what we've got first.

I certainly would not size the baseboard addition to your thermostat settings.

IMO

Zoning forced air is challenging. Zoning hydronic heat is not rocket science. Make sure you are not confusing the two. I can't imagine what kinds of "issues" that your friends might have with it. All it takes is another thermostat and either an added zone valve or circulator pump.

Here is another suggestion for you. If heat pumps are an economical choice, Install a heat pump for that area to both cool and heat it.