And what should I try now to fix it?
Let's start at the very beginning....
3-4 months ago the gravel bike went to the LBS for a service. They found some cracks in the rear rim, and built me up a new rear wheel using the original hub, new rim and spokes. All set up tubeless, all good until this morning.
Went out on the gravel bike this morning - tyres felt a little soft but put it down to two weeks riding road bikes at higher pressures.
Couple of miles in it felt too soft, so topped up both tyres. 5 miles on, rear tyre feeling soft again, stopped and put some more air in. 200 yards later, going soft again.
No sign of any air escaping, no sealant coming through. Valve a little loose in the rim, so screwed it tighter, then pumped it up and used the conveniently adjacent canal to check for any bubbles of air. Nothing coming out.
All held up, stopped at the cafe and noticed water dribbling out of the rim and some of the spoke nipples. Now it's been 30° this morning but not sure why only the rear wheel would be sweating. Presumably when the wheel was in the canal, although no air came out, water must have got in somehow?
So I have rear tyre holding air, which is a good thing, but also holding water, which is not so good. Presumably I need to get any remaining water and sealant out the tyre and top up with fresh sealant, but how do I make sure there aren't any more air leaks or water suction going on?
Pic of sweating wheel for shameless self promotion: 
I'd guess the water is in your rim not the tyre. It'll dry out.
Has it lost pressure again since you tightened the valve into the rim and tested it for leaks? If not, then it sounds like you've solved the air leak issue.
The water... I assume it'll be on the rim cavity side of the tape rather than the tyre side (i.e. not mixing with your sealant), so it'll hopefully just drain out like its doing just now...
Maybe I was overthinking it then. I will rely on your reassurance.
And come looking for you both if I get a puncture that doesn't seal but sprays the guy behind me with a 50/50 mix of Stans and stagnant canal water.....
100% this. I've done plenty of river crossings and the rim void will be full of water. Lots of rims have a drain hole, lots more don't and rely on it leaking out through the spoke holes/around the valve.I'd guess the water is in your rim not the tyre. It'll dry out.
