does sim swapping (for vacations etc) disable LTE?
No, swapping in another carrier's nano-SIM in your paired iPhone does not disable your watch's ability to use LTE as long as you are still in your carrier's network. The LTE watch can't roam. It is assigned a unique phone number from your carrier, this is what allows your watch to make native LTE calls that appear to be from your iPhone's phone number.
However, as your call is passed through your carrier's network, the phone number of your paired iPhone is assigned. Anyone that receives a call from your watch will only see your iPhone's phone number. This is why roaming is not supported since the phone number magic is done within your carrier using a specific configuration process.
if i put a different sim card into the iphone, does the LTE on the apple watch instantly stop working?
No, LTE on your watch will still work the same as long as you are within your home carrier's network. Once you leave your home carrier's coverage area your watch can't use LTE since roaming is not supported as explained above.
Or will it continue to function as much as a watch where the phone is turned off/out of power would (IIRC there are issues with SMS messages and things?)
Yes, your watch will behave as if your iPhone were powered off when your watch is out of Bluetooth or Wi-Fi range of your paired iPhone. Note: to receive SMS / MMS Txt messages on your watch when you are not in BT or Wi-Fi range of your iPhone, your iPhone must be on and connected to your carrier's network via a cellular connection or via the Wi-Fi Calling feature and your watch must have an active LTE connection. This is to allow your iPhone to receive the SMS / MMS Txts and forward it to your watch via a BT, Wi-Fi or LTE connection.
As long as your iPhone is powered on, even with a different nano-SIM and your watch is in range (BT / Wi-Fi), basic functions will continue to work since the watch depends on the iPhone for connectivity by default to conserve battery. LTE is only used as a last resort or when your force your watch to use LTE, by turning off BT and Wi-Fi.
Main thing is I want a way of making emergency calls and/or sending messages while a different sim card is in the paired iphone. I wonder would i have to activate airplane mode on the iphone or does apple watch default to its own LTE connection if the iphone has no service?
Again, your watch can only use LTE when within your home carrier's coverage area due to the "No Roaming" restriction on your watch's LTE service. You don't have to activate Airplane mode on your iPhone but you would need to turn off Bluetooth on your iPhone. Your watch can manage both Wi-Fi and LTE but Bluetooth is managed on your iPhone.
So if you are on vacation in another country, you can use your watch and make Wi-Fi calls when your iPhone is not near by if you are connecting to a "Known" Wi-Fi connection that your iPhone had already connected. When traveling, your watch will not be able to make or receive direct LTE cellular calls!
Note: once you pair your iPhone and watch and activate your watch's LTE with your carrier, then you can determine when or how to use LTE on your watch even if your switch the nano-SIM in your paired iPhone. However, your watch will not be able to use LTE unless you are still within your home carrier's service area.
Dave