What size subpanel breaker do I need?

200A in the subpanel

Which means you don't actually need a breaker; the existing 200A main breaker will suffice (assuming there actually is one, and you don't have a split-bus/Rule of Six panel).

All you need is subfeed lugs, either built into the panel, or as a bolt-in. (however, this bolt-in will take 4 breaker spaces and limit the use of breaker spaces opposite it; so prepare to move as many as 8 circuits to the new subpanel).

However, this isn't going to work...

These days, people install 200A service because the electric company won't serve anything less, so an all-gas house like mine might not even have 40A on its load calculation. Such a house could support 160A of electric tankless.

However, in the past, people installed 200A service because they had so many electric major appliances that 100A service wasn't enough. Obviously, they do not have 160A of capacity to spare... and I bet you're one of those. If you have 240V breakers on your range, dryer, furnace or A/C, I guarantee your panel does not have 160A of spare ampacity, and you'll need to either change your plan or go with a 400A-class service.

400A-class service actually implements as dual 200A service panels. So your existing 200A panel just stays put. Then you install a second 200A panel (with a LOT of extra spaces this time, please!!) And there you'll have plenty of both physical space and ampacity for your water heaters.

Is this even a good idea?

First, I think the idea of electric water heat is great, if you have the ampacity available to you. Some people don't like it, but I think most of their dislike actually relates to what I'm about to describe.

This isn't a problem you have, certainly... but many people have very bad experiences by getting too small a tankless. The heater could not carry their load (and they didn't do too much thinking about GPM and things like that). These same people also have trouble with electric cars, off-grid solar tech, and other technologies.

Then of course there's the problem you do have, which is that a successfully sized tankless can take so much electricity that it's hard to provision (at least, if other conservation measures aren't taken to reduce the needed GPM).

The hot water pipe between the water heater and the points-of-use will tend to go cold fairly quickly. As such, there's a "slug" of cold water that has to be pushed through the pipe before any hot water arrives. A centrally located tankless does nothing to improve this. However, with tankless heaters, it is possible to have multiple tankless heaters, each near a point-of-use (such as a bathroom). This eliminates the long pipe run and the waiting... and allows the local unit to be much smaller in capacity, since it only needs to support one "large" load of known size. For instance a bathroom's unit could be sized for its shower, and combined with a low-flow showerhead - making the unit size very practical. This would make the bathroom immune to temperature changes from use of hot water in other rooms (but not within the bathroom itself obviously).

An extreme of this is Great Britain's "electric shower" - an 8.5KW to 9.5KW (40A) unit that is directly attached to the shower.

The right combination of units could also reduce the overall ampacity needed, making the project more achievable.