[markem]

It makes some sense that your tank might not leak with the supply turned off. It is possible that a partial vacuum is forming within the system that is just enough to keep the (what seems to me) small leak from occurring. Open a tap and see if it still leaks. Most likely will. Either way, looks like the tank is shot.

What I have read on tankless is that it is nearly impossible to recover your costs, especially on a replacement system since idea placement is likely impossible. However, it is always best to get several places to come out, give you an estimate and discuss the options. We expect our 80 gallon tank to not last more than 3 more years as it is 11 years old (although we do regularly flush it and have little if no sediment).