For vermin to have caused an engine overheating issue, either they would have to have had to chew through a hose or radiator tank which caused loss of pressure in the system (and coolant on your garage floor) or they would have had to chew through wiring that resulted in loss or partial loss of radiator fans.
Even if vermin only chew through a coolant overflow bottle, such could result in a slower loss of coolant as the hot coolant cycles into the overflow tanks and then pours out through those chewed out holes and thus unable to get back into the system when it cools. Such may be more subtle and slower in its damaging action..
But insurance companies are funny beasts when making a claim. Often the company may want to inspect the car and if it’s been repaired they may take a dim view of it… So unless its still in an unrepaired state or you’ve got the chewed out parts and/or an receipt with clear cause of damage identified, you may have an issue… maybe… You really need to first do a good examination of the vehicle…
Once you’ve done that, then read your policy before calling your insurance company to discuss the matter. Policy wording may help guide you in how to phrase things to best support your claim
As to converter damage, well that’s usually because of a bearing, seal, clutch or structural failure of the TC itself that is the root cause. I can’t see how engine overheating can cause a TC failure (but that could be lack of imagination) and vermin can’t get to that bit of hardware… I’d think that if the tans fluid got too hot, there would be a warning message that pops up in the DIC to notify you of the problem… and I’d also think/guess it’s more likely you’d have issues with clutch bands internally to the trans rather than TC… And there is also a known weakness with early? VF? TC’s where the metal cracks as has been mentioned in another thread…