Thank you @hallett&co we are considering it but don't know what to do about adding insulation. We will need to replace the one we tear out somehow.

On our house the shingles were in pretty bad shape. We stripped the siding, added 2" of continuous rigid foam insulation, then sheathing with rain screen, sleepers, and cedar clapboards. The house is remarkably tight now, no drafts any more and very efficient to heat and cool. We also filled the stud cavities with blown in cellulose at the same time. We also had to replace the windows to accomodate the thicker walls and because they were falling apart. The house is much more comfortable as a result and is also hanging onto paint perfectly after 12 years, unlike the peeling mess we bought.

Blown in cellulose from the exterior works great.

It looks like there is existing fiberglass insulation which will preclude adding insulation in the stud cavities unless you want to remove the sheathing and fiberglass. Adding a continuous layer of exterior insulation and a vented rain screen as rwiegand described above should perform well over the long term in a northeastern climate. If the wood siding is in good shape, it can be carefully removed and salvaged. You'll need to pad out the trim at windows and doors to account for the rain screen and thicker insulation.

You have decisions to make that internet opinions can't. If you remove the vinyl + fanfold insulation, no telling how much original wood clapboards to replace or deal with lead paint. And if the windows were changed to vinyl at the same time you have some more detailing to do, as well as probably the soffits.

If you remove the original clapboards, that may kick in requirements in your location then to bring it current to code with insulation and air barrier. Which then has some detailing with windows and soffits.

Also note that "concerned about sustainability" does not confirm a decision and there are many layers that can define your stance. One could draw the line at tearing off all that vinyl and foam and sending it to the landfill, or adding more chemically made foam contributes negatively to sustainability.

You can always have it insulated by an insulation company, if necessary, but I would remove the old siding right down to nothing and put in new insulation, and no board and batten, or cedar shakes on a cape house. Use regular cedar lap siding. Try to have it look much as it looked when it was built brand new.

Test the clapboards for lead paint. Don't use a DIY test, the most common one for sale has a really high false positive rate. You can paint over lead paint, which solves the problem.