Ashamed to say without a caving operation into engine room I'm not sure what runs from what but visible batteries are 135AH 1100 CA sealed HD marine/leisure of uncertain age, over 3 years for sure. Other bank in a large covered box believed to be same ie a pair of 135AH/1100CAs
I have a trip in the aft cabin and a isolator in the bows (it's a large ceramic fuse).
Good chance the bow thruster has a battery in the bows as it is a long cable run from the engine area and current draw is very high. The battery is also spiral wound to give plates with high surface area to help it cope with the sudden demand. It is using surface charge on the plates and not discharging deeply. No impact on instruments as it is on a different circuit.
It wouldn't surprise me to find that your stern thruster isn't connected to a spiral wound battery. A normal start battery might struggle a bit as it ages and it would be even worse if connected to a deep cycle domestic bank. Not too surprised to find electronics resetting and you even hear of similar issues when starting an engine.
My boat has isolators in the aft cabin for domestic and engine. It does not have an isolator there for the battery in the bows as that wouldn't make any sense. Might as well not put a battery in the bows if you run heavy cables aft to fit an isolator.
It sounds as if the bow circuit is fine but is worth investigating to confirm the location of trips and isolators.
The stern thruster could be due to a poor battery but it is also worth check all connections. I did have a problem with a sluggish bow thruster and tracked the problem down to poor connections. It all looked fine on the surface but the dealer had not cleaned the battery posts or clamps. I found signs of arcing and pitting on the inner surfaces of the clamps. Normal service was resumed after a thorough clean and light application of Contralube 770.
To confuse me more (read totally) I just tried both thrusters with nothing else on but plugged into shorepower. Bow thruster works but stern thruster nothing happens, yesterday it worked but caused the reported disconnects. Link 20 monitor shows batteries both full and 12.6/13 vThe stern thruster itself is working normally and very powerfully, just that engaging it instantly disconnects the electronic throttles/gear controls which is disconcerting to say the least as the thrusters are only called on in awkward spots like we found revering into a very short space on fuel dock when all of a sudden we were left with both engines on tickover but no means to put them back in gear. This is when good old fashioned mechanicals would be better. Luckily simply pressing the selector button on the throttle controls turned them instantly on again (and stopped the screaming warning alarms that were very stressful).
Edited to add:-
Despite my avatar which dates back to my much loved sailing days, these days after a stroke which still leaves some albeit relatively minor problems, we are living and riding around on a Birchwood TS 37 mobo. Had we still got a very manoeuvrable single engine fin keeler with large rudder and low windage we would not need thrusters nor electronic gearshifts. Also I do not know every inch of this boat and it's systems like wot I used to on my raggies and have to rely on 'a man or two who can'