As an Aquanaut owner - the company I bought from had mine serviced by Patek before I took ownership so I won't be in a position to say exactly the service costs. The base price I think is on the Patek website.
Current prices are here (in CHF):
https://www.patek.com/en/retail-serv.../service-costs for more information.
You can choose to have the crystal replaced / strap replaced etc etc and these are additional to the service and totally up to you. You may be surprised but case polishing is an additional cost and not mandatory - which may suit some not others - you may not want it done at each service with solid gold watches.
As an example - a more complex Patek I own (5146J Annual Calendar) - last time I had it serviced with a new strap and crystal and polish after about 9 years of ownership - came to approx £1K - if you average that over the 9 years that's a bit over £100/y which I think is not bad (a lot less than my car service costs and that is worth a lot less!). They returned the old strap as well.
Servicing a mechanical watch is as important to it's long term performance regardless of brand and there are long and often bitter arguments anything between wear-them-till-they-break and get-them-serviced-every-three-years - be it Patek or Rolex. I tend to get them serviced when the timing goes off or there is an obvious fault (like pushers sticking or whatever).
Some call the Aqaunaut Patek's answer to the Seadweller (before it grew a cyclops). At 120m wrt it can certainly be worn in water and the case being slimmer than it's own clasp it is super comfortable. Comes highly recommended.
Also - How on earth did you get to handle one in the flesh?????? They have closed any waiting lists for this model last year and approximated 5years before getting one at MRP. I had to pay dealers prices - luckily before they went totally insane this year.
Holding value - come on - it's a Patek!!!
Martyn